Problems & Puzzles: Puzzles Puzzle 249. From Rudolf to Rodolfo (magic squares and pandigital numbers) In 1989 Rudolf Ondrejka (JMR, 21, Vol.1) asked:
Rodolfo Marcelo Kurchan, from Buenos Aires, Argentina, found (year?) the following answer to the Ondrejka's challenge:
Pandigital magic sum = 4129607358 Kurchan says that he found his solution without using computer. I found this magic square at the page 237 of the C. A. Pickover's 'Wonders of numbers'. But you can see it also in one of the Kurchan's pages at the web. Pickover writes:
I think that this is not so; probably the above shown magic square is the smallest magic 4x4 of that type, but it must exist some 3x3 solution. As a matter of fact I have gotten without too much pain ( because I used my PC and codes ;-) a 3x3 solution of the same type just disregarding the pandigital magic sum condition:
1023856974 1032857469 1028356479 I suspect that near to this one it should exist another solution with a pandigital magic sum (but I might be wrong!) Question 1. Find the smallest 3x3 magic square as the Kurchan' s 4x4 one (if it exist!). Question 2. Find a 3x3 magic square using only primes each having all the ten digits at least once and with the magic sum of the same type (but composite, of course!).
_________ Solution:
As a matter of fact, as I suspected there is one smaller pandigital magic sum solution in a magic 3x3 square: 1057834962 1084263579 1063549278 I got it this Sunday morning (4/1/04). It was pretty close enough the one reported before when I posed this puzzle the Saturday morning. So, my PC just worked 24 hours more and bingo!. But the problem posed by Ondrejka is a kind of old, so I also suspect that someone else should have gotten it before and of course that I'll be glad to publish the name of the first discoverer... 1089362475 1320589746 1204968537 1084793625 1327405896 1205349687
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