Can you solve our festive feast of four logic puzzles?

By Rob Eastaway, Alison Kiddle, Colin Beveridge and Steve Wain

#143 X marks the Spot

(set on 11 December) Solution

The patio requires 196 white tiles and 29 black tiles. Here’s why:

Suppose the patio is a k × k square containing a total of k2 tiles. If k is odd we need 2k – 1 black tiles and so k2 – 2k + 1=(k – 1)2 white tiles (a square number); and if k is even, (k – 1)2 – 1 (which is one less than a square). But no permutation of 1, 6 and 9 is one less than a square; so we are looking for …

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