# Arrange the numbers 1 through 10 in the shape of a pyramid

1. Feb 3, 2004

### Greg Bernhardt

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.

2. Feb 3, 2004

### meteor

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

3. Feb 3, 2004

### NateTG

It looks good, but if you're reall picky you can use the code tag for fixed spacing

Code (Text):

3
7 4
2 9 5
8 A 1 6

I wonder if the solution is unique. Apparently not:

Code (Text):

3
2 5
7 9 4
8 1 A 6

Last edited: Feb 3, 2004
4. Feb 3, 2004

### chroot

Staff Emeritus
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

5. Feb 4, 2004

### davilla

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...

6. Feb 4, 2004