I have put eight four-digit numbers together in a 4x4 grid, such that four can be read across and four downwards.

Four of my numbers are odd and four are even. I have one cubed number going across and one going down, and I have one fourth-power number going across and one going down. Two of the other numbers in the grid are squares.

Which two numbers in my grid are not perfect powers?

I constructed a set of tables within Excel of x^4 (x = 6 to 9), y^3 (y = 10 to 21) and z^2 (z = 32 to 99).

Starting with my Power 4 numbers I began compiling tables of pairs of the 4 numbers.  For each of these I then tested cubes and then squares.

By a 'jigsaw' elimination, I have the resultant grid:
4096
9025
1296
3481


These are my 8 numbers: x^4 [1296, 6561], y^3 [4096, 4913],
z^2 [3481, 9025] with 0024 and 9298 being the remaining 'not perfect powers'.

I concede that I have not gone further to see in fact there is a solution where the 10^3 digit is not zero.

Edited on July 10, 2005, 10:18 am

Posted by brianjn on 2005-07-10 10:16:30