Problems & Puzzles: Puzzles
Puzzle 69.- Primeful Heterosquares
Lets define a Primeful heterosquare as a matrix nxn, n=odd, such that:
a. The nxn inside numbers
b. The sum of every column, row & main diagonals, &
c. The sum of all the nxn inside numbers
are distinct prime numbers.
I have found (Set/98) what - I think - is the smallest 3x3 of this kind of squares, in two varieties:
a) Non consecutive primes inside
b) Consecutive primes inside
1. Can you find the smallest 5x5 & 7x7 of both kind of heterosquares?
See other Unusual Magic Squares at always interesting Harvey Heinz pages
Well, a good surprise!... Jean-Charles Meyrignac found (24/12/2000) that my first claim was wrong. He found another and smaller 3x3 primeful-heterosquare, using non-consecutive primes:
He has sent also his "best" solution for the 5x5 and the 7x7 cases:
Are these the least in its corresponding type?
Jean-Charles added: "I verified if your consecutive prime solution for puzzle 69 was the best, and it is !"
Five years later, Anurag found better results than JCM:
Least 3x3 non-Consecutive primes: sum = 139
Least 5x5 non-Consecutive :sum = 1171 [A.S. sent several; only one shown
by me, CR.]
Least 5x5 Consecutive: sum= 1259 (5..103)
Least 7x7 non-Consecutive: sum= 5119
Least 7x7 Consecutive: sum= 5813
A. S. sent larger solutions both kind...