http://bp2.blogger.com/_og40BwzbeKo/SFcfhwoeoeI/AAAAAAAAAEE/dmO7OklX8vY/s1600-h/Squares.bmp
SOLUTION:
I began by labelling the squares A-X. NB: J is the smallest square; it was too small for me to properly label!
The next step was to convert the diagram to a series of equations. These are summarised below:
(1) H=K+J
(2) I=K+2J
(3) F=2K+3J
(4) E=4K+4J
(5) G=3K+5J
(6) B=9K+12J
(7) A=13K+16J
(8) M=4K+8J
(9) L=3K+9J
(10) X=7K+17J
(11) D=10K+26J
(12) Q=P+W
(13) S=P+2W
(14) R=2P+3W
(15) T=P+3W
(16) V=4W (from Q+P+O=S+T+U)
(17) U=P+7W
(18) O=P+11W
(19) N=15W
(20) C=P+26W
(21) P=14.5W (from R+Q+T+U=S+P+N+C)
(22) 11K+14J=23.5W (from A+B=O+U)
(23) 17K+43J=47W (from D+X=A+B)
(24) K+14J=8.5W (from B+C=D+R)
(25) W=2J (from above)
(26) K=3J (from above)
Hence:
A=55J, B=39J, C=81J, D=56J, E=16J, F=9J, G=14J, H=4J, I=5J, K=3J, L=18J, M=20J, N=30J, O=51J, P=29J, Q=31J, R=64J, S=33J, T=35J, U=43J, V=8J, W=2J, X=38J
Assuming the puzzlemakers were interested in the smallest integral solution, we should let J=1, in which case the required square, X, is 38 units long #
