lionelhill
Technical User
Here's another one:
Every square number is a sum of odd numbers:
4 = 1 + 3
9 = 1 + 3 + 5
16 = 1 + 3 + 5 + 7
etc. etc.
Given a square of tiles, say 4 by 4, how many ways can you divide it into areas of 1 + 3 + 5 + 7 tiles?
(obviously an area of 7 tiles can be 7 tiles joined however you want, but it has to be one continuous shape that you could cut out of cardboard and it would be just one piece).
I think this is a nice little thing for finding the answer programatically, by trying alternatives, but I'm wondering if there is a more elegant way to do it. Before anyone feel cheated, I don't have an answer (yet).
Every square number is a sum of odd numbers:
4 = 1 + 3
9 = 1 + 3 + 5
16 = 1 + 3 + 5 + 7
etc. etc.
Given a square of tiles, say 4 by 4, how many ways can you divide it into areas of 1 + 3 + 5 + 7 tiles?
(obviously an area of 7 tiles can be 7 tiles joined however you want, but it has to be one continuous shape that you could cut out of cardboard and it would be just one piece).
I think this is a nice little thing for finding the answer programatically, by trying alternatives, but I'm wondering if there is a more elegant way to do it. Before anyone feel cheated, I don't have an answer (yet).