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Sunday Times Teaser 3039 – Three Patterned Paving

by Brian Gladman on December 18, 2020

by Howard Williams

Published Sunday December 20 2020 (links)

James is laying foot-square stones in a rectangular block whose short side is less than 25 feet. He divides this area into three rectangles by drawing two parallel lines between the longest sides and into each of these three areas he lays a similar pattern.

The pattern consists of a band or bands of red stones laid concentrically around the outside of the rectangles with the centre filled with white stones. The number of red stone bands is different in each of the rectangles but in each of them the number of white stones used equals the number of outer {1] red stones used.

The total number of stones required for each colour is a triangular number (ie, one of the form 1+2+3+…).

What is the total area in square feet of the block?

[1] this word is unnecessary (it also creates an ambiguity).

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One Comment Leave one →
  1. Brian Gladman permalink

    This solution runs in under 100 microseconds.

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