Find a 3x3 Magic Square
where the operation is MULTIPLICATION rather than addition
and the entries are 9 different numbers.
The only way I found to solve this puzzle was to use properties of EXPONENTS:
In the original problem, we were to look for an arrangement of numbers
1 through 9
that would add up to the same value in any row, column, or diagonal. One solution was this (the sum being 15):
By using the property of exponents when multiplying like bases shown above, all I have to do is choose some
raised to the values shown in each position of the array above.
The PRODUCT of each row, column, and diagonal is then:
For example, if I choose 2 for my base, I have the following array:
The PRODUCT of each row, column, and diagonal is this case:
To meet the requirement that all numbers in the array are different,
we must choose an
other than 1