The 15 Puzzle

Ok, first up, I don't want to see the solution to this, and if you write a program to crack it (not too tough) that's fine, but please don't post it here, as I'm still working on it.

It goes a little something like this. You have the integers 1-15 arranged in a triangle. Imagine a pool triangle with all the numbered balls inverted, so that the row of 5 is at the top and not the bottom. Can you arrange the numbers in such a way that each number between and below two numbers is the subtraction of those numbers. A visual example would be:

15 14 12 9 13
1 2 3 4

As you can see 15-14=1, 14-12=2, 12-9=3 and so on, until you get to the bottom of the pyramid, where it might end:

11 5
6

In the above case, the system would not work, because then 2-1 would have to equal 1, and the number 1 has already been used. Apparently there is at least one solution that allows all 15 integers to be used (only once) that satisfies the above constraints...

If any of this is not clear, and looking back on what I write it surely can't be that clear, let me know and I'll try to explain in more detail...

good luck!

joe

Holy @*!$ thats tough no wonder no one responded!😲

Here it is:

13, 3, 15, 14, 6
10, 12, 1, 8
2, 11, 7
9, 4
5

It took me almost 30 minutes, but I got it. There are probably other ways it can be done, but this is at least one of them.

didn't he ask not to post the answer LOL

Originally posted by Asher123
didn't he ask not to post the answer LOL

It had been over a year since this was posted so I thought that he should have either gotten it by now, or he gave up on it a long time ago. Therefore, it was fair game.

haha alright I didn't look at the poost dates I'll admit 😳

Wonder if there are any answers if there are 21 numbered balls and a top row of length 6...

Originally posted by iamatiger
Wonder if there are any answers if there are 21 numbered balls and a top row of length 6...

15 was ridiculously hard, I cannot imagine doing 21. I may try it later, but not now.