Mensa Math Squares Solutions

 

Check  Rows:

2 x 36 x 3 = 216

9 x 6 x 4 = 216

12 x 1 x 18 = 216

Check Columns:

2 x 9 x 12 = 216

36  x 6 x 1 = 216 

3 x 4 x 18 = 216

Check Diagonals:

2 x 6 x 18 = 216

3 x 6 x 12 = 216

B) Solution:   

Let a, b, c, d, e, f, g, h and i represent the different positive integers in the 3 x 3 grid, 

And:

a b c =  d e f = g h i = x

So: abcdefghi =  x ³

Therefore each of the nine different positive integers in the 3 x 3 grid is a factor of a cube number.   Thus:

 1¹   = 1 has factor (1)

2 ³   = 8 has four factors (1, 2, 4, 8)

3 ³   = 27 has four factors (1, 3, 9, 27)

4 ³   = 64 has seven factors (1, 2, 4, 8, 16, 32, 64)

5 ³   = 125 has four factors (1, 5, 25, 125)

6 ³   = 216 has sixteen factors (1, 2, 3, 4, 6, 8, 9,                         12, 18, 24, 27, 36, 54, 72, 108, 216)

Hence, 216 is the smallest cube with nine -plus factors.