Brain Teasers

[pgc01]

Hi Hotpepper

If the number was any other than 13 Mary would know immediately the ages of the 3 children.

Jack: Yes, I have 3. Since you always like puzzles I'll tell you like this: do you see this number on the door of the building (both look at the number), well the sum of their ages is equal to this number and the product of the ages is 36.
Mary: Can you give me something more?

So Mary knows the sum of the ages.

If the number of the building was, for ex. 14, you can check in schielrn's table that there is 1 only solution for the ages: (1,4,9).

The same for all the other possible sums: 38,21,16,11, 10.

The only case where the sum and the product are not enough to determine the 3 ages is the case of Sum=13. In that case there are 2 possibilities. Since Mary needed more information, we know that that was the case, the number on the door was 13, and Mary need more information to determine which of the 2 solutions was the one.

 

[Sandeep Warrier]

Another one...

A 3X3 chess board, with one knight on each corner. What is the minimum number of moves required to interchange the position of the knights.... (No 2 knights can occupy the same square at the same time)

Start:

Excel Workbook
	A	B	C
1
2
3
Sheet1

Excel 2003

End:

Excel Workbook
	A	B	C
1
2
3
Sheet1

Excel 2003

 

[Oorang]

Hmmm, there may be a more optimum solution but simple rotation yields the swap in 16 moves.

 

[Cindy Ellis]

Oops....no longer relevant!

 

[yytsunamiyy]

Another one...

A 3X3 chess board, with one knight on each corner. What is the minimum number of moves required to interchange the position of the knights.... (No 2 knights can occupy the same square at the same time)

Start:

Excel Workbook
	A	B	C
1
2
3
Sheet1

#VALUE!

Excel 2003

The absolute minimum number of moves would be one. Either you move around the board or you move the board through 180°.

 

[Gettingbetter]

I can do it in 8, surely theres no quicker way than that, I hope there is that would be interesting.

 

[Sandeep Warrier]

I can do it in 8, surely theres no quicker way than that, I hope there is that would be interesting.

Could you post the 8 moves???
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[Oaktree]

I'm with Oorang on that one, it looks like 16 to me.

 

[pgc01]

Nice one Sundeep.

Until now I also can only do it in 16 moves.

 

[arkusM]

I can do it in 16 as well.