Enigma 1680: Do magic
11 January 2012
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From New Scientist #2847, 14th January 2011 [link]
I have constructed a 3×3 magic square – that is, it contains nine different whole numbers and each row, column and main diagonal has the same sum. But my numbers are in a base other than 10 and I have used letters for the higher “digits”, namely A for 10, B for 11, C for 12, and so on, as far as necessary. The result is that one of the entries in my square now reads as “DO” (the letters D and O) and the bottom row of the square, when read right across, makes the word “MAGIC”.
In decimal notation, (a) What base was I working in? (b) What is the sum of each row?