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Problem of the Week 1064

A Magic Nonsquare

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In the Lo Shu magic square shown here, the sum of any 3 digits in a straight line is 15.

These are the 8 ways in which 15 can be written as the sum of 3 nonzero digits.

Find a new layout in which the same digits, relocated to new positions, again form 8 collinear triads of equal sum, but with this common sum not equal to 15. What is the least number of circles that must be relocated to achieve this?

Source: This is a new and original problem of Lee Sallows (Nijmegen, The Netherlands). I would like to know whether this problem is considered difficult, easy, or medium, so feel free to comment. It is noteworthy that Lee has found something original to say about this most ancient of magic squares.

© Copyright 2006 Stan Wagon. Reproduced with permission.

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19 October 2006