From Andy Biddulph
Your article on brain training included the puzzle below (12 January, p 26). You give the answer as 53, apparently by numbering the rows and columns starting at the bottom right corner, and appending the row number to the column number.
Another solution would be: the first digit in one column plus the first digit in the next-but-one column always add up to 10.
This would mean the first digit in each column is, from left to right: 9, 6, 1, 4, 9, 6, 1.
To find the second digit look at the row instead – the second digit in one row and the second digit in the next-but-one row add up to 6.
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Therefore the second digit in each row, from top to bottom, is 1, 2, 5, 4, 1, 2, 5. This gives the answer 11.
A simpler solution is to assume that the numbers in any given column are the same.
Subtracting 45 from 64 gives us 19, so go from right to left adding 19 to get the next-but-one column. The rows, right to left, are then 12, 26, 31, 45, 50, 64, 69. The answer is now 50.
A large – if not infinite – number of rules can be devised to generate any set of numbers placed arbitrarily on any grid or n-dimensional array.
There is no a priori reason to choose any of these rules, so problems of this type test only “can you spot the arbitrary choice made by the person devising the problem?”
Burton on Trent, Staffordshire, UK
