PUZZLE 36
DIGITS AND CUBES
My Professor recently asked his young friends to find all those five-figure squares such that the number formed by the first two figures added to that formed by the last two figures should equal a cube. Thus with the square of 141, which is 19,881, if we add 19 and 81 together we get 100, which is a square but unfortunately not a cube. How many solutions are there altogether?
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The Mathemagician Arena Alabi Stephen is an expert in recreational mathematics. A self trained, adept mathemagician. All this he can do mentally.
He combines his love for maths and magic to do what he calls- Mathemagics. Stephen can compute and complete in his head within splits of seconds many mathematical feats. Ranging from addition, multiplication, squares, cubes, square roots, cube roots, and 5th roots of numbers to other complex equation. Better still, he'll show you how he learned to throw away the pencil, paper, Biro and calculator to create Mathemagic.
SOLUTION TO PUZZLE 35
THREE DIFFERENT DIGITS
The numbers are 162, 243, 324, 392, 405, 512, 605, 648, 810, and 972. These, I think, are all the cases that exist.
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