A super number square has the following properties:
- In each row, the rightmost number is the sum of the other three.
- In each column, the bottom number is the sum of the other three.
- Within each NW-SE diagonal line, the last number (bottom rightmost) is the product of the other numbers.
For example, if you have a square that looks like:
A B C D
E F G H
I J K L
M N P Q
you know that A+B+C=D, C+G+K=P, AFK=Q, EJ=P, and so on.
Construct a super number square in which the highest number in any position is 57, and the second number in the top row is a 5 (all numbers are positive integers).
My analysis reveals a great number of solutions for example:
1, 5, 4,10 3, 5, 4,12 1, 5, 1, 7 1, 5, 7,13
2, 3, 7,12 2, 1, 7,10 1,19, 5,25 1,19, 4,24
1,15,19,35 1,15,19,35 13, 9, 3,25 3,14, 3,20
4,23,30,57 6,21,30,57 15,33, 9,57 5,38,14,57
Many more solutions can be generated by rearranging the numbers in the AFK diagonal (1,3,19 - the factors of 57), and building equations and inequalities from the remaining variables (C,G,E,I,and J). The two major equations evolve from EJ=C+G+K(1,3,or 19) and 5G=I+J+K. The major inequalities are built from the fact that all variables are between 1 and 57.
|
|
Posted by Eric
on 2003-09-05 02:17:34 |
solution
