PRIZE PUZZLE FOR NOVEMBER 2007
I have a rectangular block of wood (that is, each of the six faces are rectangles). The diagonals across the faces measure exactly 40, 43 and 51 mm. What is the length of the diagonal across the centre of the block?
If A,B,C are the squares of the three sides, the answer is the square-root of A+B+C. We don't need to work out the sides, which are irrational numbers. Pythagoras tells us that: A+B = 40 x 40 = 1600 B+C = 43 x 43 = 1849 A +C = 51 x 51 = 2601 Adding these three equations: 2A+2B+2C = 1600+1849+2601 = 6050 halving A+B+C = 3025 so the answer is the square root of 3025 which is 55.
I received only one answer, from John Stafford, so there was no draw this month. Thanks to John for his analysis of the problem.