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?

The two that are not perfect powers are 2316 and 9738. My VB program established this as the only answer. The two grids below (each is the equivalent of the other with columns and rows switched) are the only possibilities: 

-------------------------
1 2 9 6
3 3 7 5
3 1 3 6
1 6 8 1 
    
4-Powers (also Squares): 1296 6561  
Cubes: 1331 3375
Other Squares: 3136 1681  
Not Perfect Powers: 2316 9738

-------------------------
1 3 3 1
2 3 1 6
9 7 3 8
6 5 6 1 
    
(Same)

 

 

 

 

Edited on October 20, 2007, 10:31 am

Posted by Penny on 2005-07-11 01:09:48