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Sunday Times Teaser 3223 – Shaping Up

by BRG on June 28, 2024

by Peter Good

Published Friday June 28 2024 (link)

Clark wondered how many different shapes he could draw with identical squares joined edge to edge and each shape containing the same number of squares. He only drew five different shapes containing four squares, for example, because he ignored rotations and reflections (see diagram, above). He drew all of the different shapes containing 1, 2, 3, 4, 5 and 6 squares and wrote down the total number of different shapes in each case. He took the six totals in some order, without reordering the digits within any total, and placed them end to end to form a sequence of digits which could also be formed by placing six prime numbers end to end.

In ascending order, what were the six prime numbers?

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  1. BRG permalink


    This teaser is partly about counting the numbers of plane figures that can be formed using a number of edge connected unit squares. Such figures, which are known as Polyominoes, are well researched and are described in some detail at Wikipedia and Mathworld.

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