math puzzle HELP!!!?

Question

The puzzle says that you have to draw 15 circles like this:
( )( )( )( )( )
( )( )( )( ) You have to put the numbers 1-15 into it.
( )( )( ) You can't use any number twice
( )( ) and you have to subtract the two numbers
( ) like this :

(15) - (14) - (2) - ( 8 ) - ( 3 )
( 1 ) - (12) - ( 6 ) - ( 5 )

15 - 14 = 1, the 1 goes directly below the two numbers.
(15) - (14) - (2) - ( 8 ) - ( 3 )
( 1 )
14 - 2 = 12 ,the 12 goes directly below the two numbers.
(15) - (14) - (2) - ( 8 ) - ( 3 )
( 1 ) - (12)
12 - 8 = 4, the 4 goes directly below the two numbers.
(15) - (14) - (2) - ( 8 ) - ( 3 )
( 1 ) - (12) - ( 6 )
8 - 3 = 5, the 5 goes directly below the two numbers.
(15) - (14) - (2) - ( 8 ) - ( 3 )
( 1 ) - (12) - ( 6 ) - ( 5 )
And so on and so fourth.

Please help,
John

Answer 1

With a *lot* of thought, you can work this out logically. It's an old, classic puzzle (originally done with racking billiard balls, I believe). I did a quick web search, but didn't pick the right keywords for finding a description of the solution.

15 *must* go in the top row, as there is no way to generate the difference from the other 14 numbers. Similarly, 14 must appear either in the top row or just under 15-1.

You might try a web search of your own, now that you know it's a solved problem in the puzzle literature. I expect that it's in the FAQ list of rec.puzzles (an oooold newsgroup).

I'm sorry I don't have time to find the answer for you; I have to get back to work.

Answer 2

Math puzzles/games