Horse Racing Combinations - Trifecta (Without Macro)

[jmcalabaza]

Hello Everyone!

Well, I am trying to gather all possible combinations for 10 horses for 3 place finishers. The 3 place finish is to illustrate a trifecta ticket. Example:

1-2-3
1-2-4
1-2-5
1-2-6
.
.
.
2-3-6
2-4-5
2-8-9


I understand for 10 horses, I should have a total of 720 combinations for a trifecta group. I really need help and I cannot figure out what formulas to use to achieve this. Also, I would like the formula to immediately toss out duplicates like (1-2-2, 2-2-4, etc.) in which that the #2 horse cannot finish in 2nd or 3rd place - only one place.

Thank you for your attention to this headache and I hope to hear from someone soon!

Jon

 

[StephenCrump]

Welcome to the Forum!

Much easier with VBA, but try these formulae, copied down the columns:

B2: =1+MOD(A2-1,NoHorses)
C2: =MOD(INT((A2-1)/NoHorses),NoHorses-1)+IF(1+MOD(INT((A2-1)/NoHorses),NoHorses-1)>=B2,1,0)+1
D2: =INT((A2-1)/NoHorses/(NoHorses-1))+1+IF(1+MOD(INT((A2-1)/NoHorses/(NoHorses-1)),NoHorses)>=MIN(B2:C2),IF(MOD(1+INT((A2-1)/NoHorses/(NoHorses-1)),NoHorses)+1>=MAX(B2:C2),2,1),0)

where NoHorses=10

The pattern will be easier to see if you Copy/Paste Values, and then sort on Column B/Column C.

Excel 2010

	A	B	C	D
Combinations

<tbody>
[TD="align: center"]1[/TD]

[TD="align: right"]1st[/TD]
[TD="align: right"]2nd[/TD]
[TD="align: right"]3rd[/TD]

[TD="align: center"]2[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]3[/TD]

[TD="align: center"]3[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]3[/TD]

[TD="align: center"]4[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]

[TD="align: center"]5[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]

[TD="align: center"]6[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]

[TD="align: center"]7[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]

[TD="align: center"]8[/TD]
[TD="align: right"]7[/TD]
[TD="align: right"]7[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]

[TD="align: center"]9[/TD]
[TD="align: right"]8[/TD]
[TD="align: right"]8[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]

[TD="align: center"]10[/TD]
[TD="align: right"]9[/TD]
[TD="align: right"]9[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]

[TD="align: center"]11[/TD]
[TD="align: right"]10[/TD]
[TD="align: right"]10[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]

[TD="align: center"]12[/TD]
[TD="align: right"]11[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]2[/TD]

[TD="align: center"]13[/TD]
[TD="align: right"]12[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]1[/TD]

[TD="align: center"]14[/TD]
[TD="align: right"]13[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]1[/TD]

[TD="align: center"]15[/TD]
[TD="align: right"]14[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]1[/TD]

[TD="align: center"]16[/TD]
[TD="align: right"]15[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]1[/TD]

[TD="align: center"]17[/TD]
[TD="align: right"]….[/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]
[TD="align: right"][/TD]

[TD="align: center"]18[/TD]
[TD="align: right"]720[/TD]
[TD="align: right"]10[/TD]
[TD="align: right"]9[/TD]
[TD="align: right"]8[/TD]

</tbody>

Sheet1​

 

[jmcalabaza]

Stephen!

Thank you so much for this information. This helps a lot!

Have a great day Sir!

Jon