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Square Power (Posted on 2005-07-10) Difficulty: 4 of 5
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?

No Solution Yet Submitted by Sam    
Rating: 4.5000 (2 votes)

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Solution Is a two digit number a 4 digit one? | Comment 1 of 7
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:

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

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