[Guest]

in the classic no-where neat puzzle, you start with a large square, and try to fit as many smaller squares as you can in it such that no two squares of the same size share a full edge. my question is this: is it possible to construct an etirely prime no-where neat square? that is: the large square side length is prime, and all the smaller squares inside have a prime length edge?

i suspect the answer to be yes, but have yet to find such a solution.

[curr3nt]

Are the lengths of the sides restricted to integer values > 1?

If so then a 3x3 square with one 2x2 square inside it. If not then the number of squares inside will be infinity or have sides of length 1 which isn't prime

in the classic no-where neat puzzle, you start with a large square, and try to fit as many smaller squares as you can in it such that no two squares of the same size share a full edge. my question is this: is it possible to construct an etirely prime no-where neat square? that is: the large square side length is prime, and all the smaller squares inside have a prime length edge?

i suspect the answer to be yes, but have yet to find such a solution.

[Guest]

sorry i should clarify the whole square is filled, no space left over. (so yes only integer side length, 2,3,5,7,11 etc.)

Edited January 21, 2011 by phillip1882

[k-man]

I didn't solve this myself, but while looking up what the heck "ho-where neat puzzle" means I found this example which fit the requirement of the puzzle. Red squares are size 1, blue - 2, yellow - 3, cyan - 5, magenta - 7. The total square is 19x19. All prime numbers!

EDIT: Well, 1 is not a prime number, so this is probably not a valid solution.

Edited January 21, 2011 by k-man

[Guest]

right 1 is not prime so invalid.

[curr3nt]

That means a 2x2 square can't be used.

right 1 is not prime so invalid.

[Guest]

sure it can, 2 is prime.

[curr3nt]

sure it can, 2 is prime.

If a 2x2 exists then either a 1x1 exists or another 2x2 has to be next to it. Doesn't it?

[Guest]

obviously if two is near an edge i would agree. but you could have 2 near the center of a fairly large square and make it work, i think...

for example, something like this...