How many ways the numbers 1 to 7 can be arranged to get sum = 7

M

motilulla

Well-known Member
Joined
Feb 13, 2008
Messages
2,422
Office Version
  1. 2010
Hi everybody,

how many total ways could be possible to arrange numbers from 1 to 7 to get always sum = 7. Below is shown few ways in the example table: <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p>
<o:p></o:p>
Example Table: Sum = 7<o:p></o:p>
<TABLE style="WIDTH: 235pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0cm 0cm 0cm 0cm" border=0 cellSpacing=0 cellPadding=0 width=313><TBODY><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; WIDTH: 25pt; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom width=33 noWrap>*<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; WIDTH: 25pt; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom width=33 noWrap>A<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; WIDTH: 25pt; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom width=33 noWrap>B<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; WIDTH: 25pt; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom width=33 noWrap>C<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; WIDTH: 25pt; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom width=33 noWrap>D<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; WIDTH: 25pt; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom width=33 noWrap>E<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; WIDTH: 25pt; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom width=33 noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; WIDTH: 25pt; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom width=33 noWrap>G<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; WIDTH: 35pt; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom width=47 noWrap>H<o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; BACKGROUND: yellow; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; BACKGROUND: yellow; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>2<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; BACKGROUND: yellow; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>3<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; BACKGROUND: yellow; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>4<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; BACKGROUND: yellow; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>5<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; BACKGROUND: yellow; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>6<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; BACKGROUND: yellow; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; BACKGROUND: yellow; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>Sum 7<o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>2<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>3<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>2<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>4<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>2<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>3<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>5<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>2<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>2<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>6<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>2<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>2<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>3<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>2<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>3<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>8<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>5<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>1<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>9<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>5<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>2<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>10<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>11<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>12<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt"><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>13<o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap> <o:p></o:p>
</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: #ece9d8; PADDING-BOTTOM: 0cm; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0cm; PADDING-RIGHT: 0cm; HEIGHT: 12.75pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 0.5pt solid; PADDING-TOP: 0cm" vAlign=bottom noWrap>7<o:p></o:p>
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Is it possible to list total ways that could make sum of 7?<o:p></o:p>


<o:p></o:p>
Thanks And Regards,
Moti
 
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I guess I have taken his list of 63 combinations as the better guide to his intentions (post #6).
 
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motilulla said:
Hi mirabeau,<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p>
<o:p></o:p>
I’ am grateful for your kind attention and for giving a code solution. Of course code solution is a best way to list the combinations rapidly. But unfortunately I have still excel version 2000. After running the code line below highlighted in yellow it gives the following error: Out of memory (Error 7)
<o:p></o:p>
Code: 
ReDim y(1 To n ^ v, 1 To v)
<o:p></o:p>
<o:p></o:p>
Please, is it possible to have a code for excel version 2000?<o:p></o:p>
<o:p></o:p>
Thanks and Regards,<o:p></o:p>
Moti
Click to expand...
Hi Moti,

Here's a couple of posts which I hope you find of some interest.

This one lists the output of the code I posted giving ways of summing to 7. This gives 64 ways.

If there's more combinations that occur to you that are not included here (1516 or whatever) then the next post, containing an equivalent code that you should be able to run OK, may be of some help in clarifying.
7
1 6
2 5
3 4
4 3
5 2
6 1
1 1 5
1 2 4
1 3 3
1 4 2
1 5 1
2 1 4
2 2 3
2 3 2
2 4 1
3 1 3
3 2 2
3 3 1
4 1 2
4 2 1
5 1 1
1 1 1 4
1 1 2 3
1 1 3 2
1 1 4 1
1 2 1 3
1 2 2 2
1 2 3 1
1 3 1 2
1 3 2 1
1 4 1 1
2 1 1 3
2 1 2 2
2 1 3 1
2 2 1 2
2 2 2 1
2 3 1 1
3 1 1 2
3 1 2 1
3 2 1 1
4 1 1 1
1 1 1 1 3
1 1 1 2 2
1 1 1 3 1
1 1 2 1 2
1 1 2 2 1
1 1 3 1 1
1 2 1 1 2
1 2 1 2 1
1 2 2 1 1
1 3 1 1 1
2 1 1 1 2
2 1 1 2 1
2 1 2 1 1
2 2 1 1 1
3 1 1 1 1
1 1 1 1 1 2
1 1 1 1 2 1
1 1 1 2 1 1
1 1 2 1 1 1
1 2 1 1 1 1
2 1 1 1 1 1
1 1 1 1 1 1 1
 
Upvote 0
Hi

In case the result is the 64 ways a group of numbers adds up to 7 that was posted before, here's an alternative code.

It takes in my PC abount 1/100 second to execute.

Code: 
Sub Gen()
Dim s As String
Dim vArr As Variant
Const N As Long = 7
 
genstr s, "", N, 1, 0
vArr = Split(Mid(s, 2), ",")
Range("A1").Resize(UBound(vArr) + 1).Value = Application.Transpose(vArr)
End Sub
 
Sub genstr(ByRef sRes As String, ByVal sTmp As String, ByVal N As Long, ByVal lInd As Long, ByVal lSum As Long)
Dim i As Long
 
For i = 1 To N - lInd + 1
    If lSum + i > N Then Exit For
    If lSum + i < N Then
        genstr sRes, sTmp & " " & i, N, lInd + 1, lSum + i
    Else
        sRes = sRes & "," & Trim(sTmp & " " & i)
    End If
Next i
End Sub
 
Upvote 0
pgc01 said:
Hi

In case the result is the 64 ways a group of numbers adds up to 7 that was posted before, here's an alternative code.

It takes in my PC abount 1/100 second to execute.

Code: 
Sub Gen()
Dim s As String
Dim vArr As Variant
Const N As Long = 7
 
genstr s, "", N, 1, 0
vArr = Split(Mid(s, 2), ",")
Range("A1").Resize(UBound(vArr) + 1).Value = Application.Transpose(vArr)
End Sub
 
Sub genstr(ByRef sRes As String, ByVal sTmp As String, ByVal N As Long, ByVal lInd As Long, ByVal lSum As Long)
Dim i As Long
 
For i = 1 To N - lInd + 1
    If lSum + i > N Then Exit For
    If lSum + i < N Then
        genstr sRes, sTmp & " " & i, N, lInd + 1, lSum + i
    Else
        sRes = sRes & "," & Trim(sTmp & " " & i)
    End If
Next i
End Sub
Click to expand...

Nice 1 m8
 
Upvote 0
Hi, xenou as shg has explained in post #19 there are seven distinct variables and pgc01 said in post #20 that my opening post shows 7-column grid. According to that moving 7 numbers in 7 columns can be arrange in 1716 ways. It is correct.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p>
<o:p></o:p>
I have Used mirabeau code and removed number 7 from array now it generate 1709 combination instead of 1716 and 7 missing combination are of 7 numbers.<o:p></o:p>
Run the code below on a blank sheet it will generate 1709 combination:<o:p></o:p>
Rich (BB code):
Rich (BB code):
Rich (BB code):
Rich (BB code): 
Sub sumtoseven_All()
Dim valz, y() As Long, n&, v&
Dim a&, b&, c&, d&, k#
valz = Array(0, 1, 2, 3, 4, 5, 6)
n = UBound(valz) + 1: v = n
ReDim y(1 To n ^ v, 1 To v)
For a = 1 To v
 For b = 1 To n ^ v Step n ^ a
     For c = b To b + n ^ (a - 1) - 1
         For d = 1 To n
             y(c + n ^ (a - 1) * (d - 1), v - a + 1) = valz(d - 1)
Next d, c, b, a
For i = 1 To n ^ v
s = 0
For j = 1 To v: s = s + y(i, j): Next j
If s = 7 Then
 k = k + 1
 For j = 1 To v: y(k, j) = y(i, j): Next j
End If
Next i
With Range("A1").Resize(k, v)
 .Cells = y
End With
End Sub
<o:p></o:p>
<o:p></o:p>
<o:p></o:p>
<o:p></o:p>
<o:p></o:p>
<o:p></o:p>
Run the code below on a blank sheet it will generate 64 unique combinations:<o:p></o:p>
Rich (BB code):
Rich (BB code):
Rich (BB code):
Rich (BB code): 
Sub Sumtoseven_Unique()
Dim valz, y() As Long, n&, v&
Dim a&, b&, c&, d&, k#
valz = Array(0, 1, 2, 3, 4, 5, 6)
n = UBound(valz) + 1: v = n
ReDim y(1 To n ^ v, 1 To v)
For a = 1 To v
 For b = 1 To n ^ v Step n ^ a
     For c = b To b + n ^ (a - 1) - 1
         For d = 1 To n
             y(c + n ^ (a - 1) * (d - 1), v - a + 1) = valz(d - 1)
Next d, c, b, a
For i = 1 To n ^ v
s = 0
For j = 1 To v: s = s + y(i, j): Next j
If s = 7 Then
 k = k + 1
 For j = 1 To v: y(k, j) = y(i, j): Next j
End If
Next i
With Range("A1").Resize(k, v)
 .Cells = y
 .Replace 0, ""
 .SpecialCells(4).Delete xlToLeft
 
 Range("A1:G1709").Select
 Range("A1:G1709").AdvancedFilter Action:=xlFilterInPlace, Unique:=True
 Selection.Copy
 Range("I1").Select
 ActiveSheet.Paste
 Application.CutCopyMode = False
 ActiveSheet.ShowAllData
 Columns("I:O").Select
 Selection.Copy
 Range("A1").Select
 ActiveSheet.Paste
 Columns("I:O").Select
 Application.CutCopyMode = False
 Selection.Delete Shift:=xlToLeft
 Range("A1").Select
End With
End Sub
<o:p></o:p>
<o:p></o:p>
<o:p></o:p>
<o:p></o:p>
I think now things are bit clear with sum seven either 64 or 1716 can be made.<o:p></o:p>
<o:p></o:p>
While replying this post I saw that pcg01 has facilitated code. I tried it out and it is fast and fantastic solution.<o:p></o:p>
<o:p></o:p>
Thanks And Regards,<o:p></o:p>
Moti<o:p></o:p>
 
Last edited:
Upvote 0
Hey Moti,

Here's follow-up code as earlier indicated.
The code in Post#9 is very inefficiently written for this particular task. That's because I wrote its basics about 18 months ago for a different purpose and have had it lying around the attic since then without modification. Funny thing, I've conveniently used it again several times in different threads over the past few weeks.

That Post#9 code will run you out of memory very quickly as it was posted. My computer handles it OK.

But it should work OK for you if you consider the equivalent ways of summing to 5, rather than to 7. Maybe might clarify just what you want.
So try this modified version.
Rich (BB code): 
Option Explicit
Sub sumtofive()
Dim dic As Object
Dim valz, y() As Long, n&, v&, s&
Dim a&, b&, c&, d&, k#, xx As String
valz = Array(0, 1, 2, 3, 4, 5)  'changed to 5
n = UBound(valz) + 1: v = n
ReDim y(1 To n ^ v, 1 To v)
For a = 1 To v
    For b = 1 To n ^ v Step n ^ a
        For c = b To b + n ^ (a - 1) - 1
            For d = 1 To n
                y(c + n ^ (a - 1) * (d - 1), v - a + 1) = valz(d - 1)
Next d, c, b, a
For a = 1 To n ^ v
s = 0
For b = 1 To v: s = s + y(a, b): Next b
If s = 5 Then   'changed to 5
    k = k + 1
    For b = 1 To v: y(k, b) = y(a, b): Next b
End If
Next a
Set dic = CreateObject("scripting.dictionary")
For a = 1 To k
    xx = vbNullString
    For b = 1 To v
        If y(a, b) <> 0 Then xx = xx & Chr(30) & y(a, b)
    Next b
    If Not dic.exists(xx) Then
        dic.Add xx, vbNullString
        For b = 1 To v:  y(dic.Count, b) = y(a, b): Next b
    End If
Next a
[a1].Resize(dic.Count, v) = y
End Sub
To see two of the interpretations that seem to have been given of what you asked for (with zeros included), you can run the code twice, once with the red part included, then delete the red part and run it again.

However, VBA codes are only interpretations of what the user wants, and can't necessarily be taken any more seriously than other sources of information.

In your case, what you actually want seems, from previous posts, well described by a line from Franz Kafk'a story "The Great Wall of China" die gemeinsame Unsicherheit in dieser Hinsicht ist so groß, dass selbst die besten Schülerinnen und Schüler darin gezeichnet werden
 
Upvote 0
Mirabeau, tried your code changing sum up to 6 and it generate 924 combination but it fails at sum 7 and give error out of memory I think it should be ReDim after certain rows. Which is missing in the code.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p>
<o:p></o:p>
All the way making it "The Great Wall of China" we have come up to the solution. For that I want to thanks all of you, for assisting collaborating and giving their opinion and correct solutions.<o:p></o:p>
<o:p></o:p>
And special thanks; to pgc01 for giving a nice code solution<o:p></o:p>
<o:p></o:p>
Thanks And Regards,<o:p></o:p>
Moti<o:p></o:p>
 
Upvote 0
yes, pgc01 - your code is quite a nice piece of vba wizardry.
 
Upvote 0
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