Enigma 1303: Lucky numbers
8 August 2014
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From New Scientist #2461, 21st August 2004
Alex and his big sister Monica were using a new method to work out their lucky numbers. First they chose at random a number from 1 to 26 and assigned that value to the letter A. They then valued each of the remaining letters B to Z, with a number relating to its position in the alphabet. For example, if A had been given the value 10, then B would be 11, C would be 12, and so on through to Q=26, R=1 … Z=9.
With this exercise complete, they added up the totals for their respective names to find their lucky numbers. Alex was delighted, because (A+L+E+X) was bigger than (M+O+N+I+C+A). And they were both pleased to find that when the two lucky numbers were added together they made a perfect square.
What was the original value chosen for A?