**From New Scientist #1483, 21st November 1985** [link]

My calculating nephew has been foxing me again. He entered a three-figure number on the calculator, showed it to me, and then squared the number but tried to trick me by showing me the square upside down.

I could soon see that there was something wrong because although I could see a number it had no digits in common with the number that had been squared — whereas I know that their first digits should have been the same. Further investigation would have shown that the original number and its inverted square had no factors larger than 1 in common.

Now, without a computer, and without hours of work, you should be able to tell me what I want to know. What was the original three-figure number? And what number did my nephew show me trying to kid me that it was the square?

[enigma335]

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Obviously I did use a computer, but not hours of time. This Python program runs in 44ms.

Solution:The original 3-digit number was 953. The inverted square that the nephew showed was 602806.