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## Brain Teaser #78

Arrange the numbers 1 through 10 in the shape of a pyramid (1 number at the peak, 2 numbers in the next row down, 3 in the next row, and 4 in the bottom row). The numbers must be arranged such that each number is equal to the difference of the two numbers directly below it. For example, if 5 and 1 are next to each other in the same row, then 4 must be placed on top of them.
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 Blog Entries: 4 3 7 4 2 9 5 8 10 1 6 It represents a pyramid, though I'm unable to give to it a pyramidal shape
 Recognitions: Homework Help Science Advisor It looks good, but if you're reall picky you can use the code tag for fixed spacing Code:  3 7 4 2 9 5 8 A 1 6 I wonder if the solution is unique. Apparently not: Code:  3 2 5 7 9 4 8 1 A 6

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## Brain Teaser #78

There are eight solutions:

{3, 2, 5, 7, 9, 4, 8, 1, 10, 6},
{3, 4, 7, 5, 9, 2, 6, 1, 10, 8},
{3, 5, 2, 4, 9, 7, 6, 10, 1, 8},
{3, 7, 4, 2, 9, 5, 8, 10, 1, 6},
{4, 1, 5, 6, 7, 2, 9, 3, 10, 8},
{4, 2, 6, 5, 7, 1, 8, 3, 10, 9},
{4, 5, 1, 2, 7, 6, 8, 10, 3, 9},
{4, 6, 2, 1, 7, 5, 9, 10, 3, 8}

- Warren
 For 1 level, there are 4 solutions: 2 / 1 3 2 / 3 1 1 / 2 3 1 / 3 2 3 always appears on the bottom. For 2 levels, there are 6 solutions: 2 / 3 5 / 4 1 6 2 / 5 3 / 6 1 4 1 / 3 4 / 5 2 6 1 / 4 3 / 6 2 5 3 / 4 1 / 2 6 5 3 / 1 4 / 5 6 2 6 always appears on the bottom. 5 and 4 appear on the bottom two levels, with only one of these at the highest. I trust there are no more than 8 solutions for 3 levels: 3 / 4 7 / 5 9 2 / 6 1 A 8 3 / 7 4 / 2 9 5 / 8 A 1 6 3 / 2 5 / 7 9 4 / 8 1 A 6 3 / 5 2 / 4 9 7 / 6 A 1 8 4 / 2 6 / 5 7 1 / 8 3 A 9 4 / 6 2 / 1 7 5 / 9 A 3 8 4 / 1 5 / 6 7 2 / 9 3 A 8 4 / 5 1 / 2 7 6 / 8 A 3 9 10 always appears on the bottom. 8 and 9 appear on the bottom two levels. (In fact 8 is always on the bottom.) 5, 6, and 7 appear on the bottom three levels, with only one of these at the highest. What a great way to waste time...
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