Today Puzzle #591
Puzzle No. 591 – Thursday 17 October
Three Standard dice are stacked in a tower so that the numbers on each pair of touching faces add to 5. The number on the top of the tower is even. What is the number on the base of the tower?
Today’s #PuzzleForToday has been set by Senior Kangaroo mathematics competition, run in the UK by the UK Mathematics Trust.
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First not that, on a standard die, the number on opposite faces add to 7. Let the number on the top of the tower by n. The numbers on the touching faces going down the tower are then 7-n, 5-(7-n)=n-2, 7-(n-2)=9-n and 5-(9-n)=n-4 respectively. The bottom number is 7-(n-4)=11-n. The number on a dies are 1 to 6 so 11-n<6 and hence n>5. The question states that n is even so n=6. Hence the number on the bottom of the tower is 11-n=5. (It is easy to check that when n=6 all the numbers going down the tower are values that can appear on the face of a standard die.