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Sunday Times Teaser 3106 – Underground Umbra Conundrum

by Brian Gladman on April 2, 2022

by Stephen Hogg

Published Sunday April 03 2022 (link)

 

An underground car park has rectangular walls, each covered with 300 abutting square tiles arranged in three repeats of red, orange, yellow, green and blue columns twenty tiles high. A sharp tapering shadow from a duct played across one wall from top to bottom (with straight lines similar to that shown).

Each shadow edge crossed every colour and, curiously, hit just two points where four tile corners met. The upper and lower pairs of these were on levels the same distance up and down from the mid-level line. I also noticed that no column was completely free of shadow, but just one column was completely in shadow.

Give the shadow’s area relative to the wall area as a fraction in simplest form.

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  1. Brian Gladman permalink

    This solution runs in 160 milliseconds with profile timing and finds two solutions with the same area. Its performance can be improved to 55 milliseconds by using the GMPY2 rational implementation in place of the standard Python fractions module.

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