Sunday Times Teaser 2753 (2015-06-28)

puzzle.txt

sign
	l = length in cm
	w = width in cm

l = 2w

(sum length digits)^2 - l = w

(sum width  digits)^2 - w = l

solve.sh

#!/bin/bash

for ((WIDTH = 1; WIDTH < 100; WIDTH++)); do
	LENGTH=$((WIDTH*2))

	LDIGITS=$(( $(echo $LENGTH | sed -e 's/./+&/g') ))
	LD_SQUARE=$((LDIGITS*LDIGITS))
	LD_RESULT=$((LD_SQUARE - LENGTH))
	[ $LD_RESULT -lt 0 ] && continue;

	WDIGITS=$(( $(echo $WIDTH | sed -e 's/./+&/g') ))
	WD_SQUARE=$((WDIGITS*WDIGITS))
	WD_RESULT=$((WD_SQUARE - WIDTH))
	[ $WD_RESULT -lt 0 ] && continue;

	[ $LD_RESULT = $WIDTH ] && [ $WD_RESULT = $LENGTH ] && echo ${LENGTH}x${WIDTH}cm
done