Enigma 388: See the light!
17 March 2017
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From New Scientist #1537, 4th December 1986 [link]
My niece was playing with my calculator recently. She showed me a three-figure number displayed (and I could see three different digits) and then she pushed the “square” button. This resulted in another number being displayed. I could see a number, but I soon realised that it was not the square of the original number.
On investigation we soon find out what was wrong. My calculator usually lights up the digits in this way:
that is, it lights up some of the seven little elements in each case. But we found out that the calculator had developed a fault. Although it did all its calculations correctly, in each place where a digit could be displayed the same one of the seven elements never lit up.
Some digits from 0 to 9 could still be lit up correctly, but over half of them couldn’t. Just that fact, together with knowing how many of the 10 digits could light up correctly, would enable you to work out which of the seven elements consistently failed.
If my calculator had been working correctly, what would I have seen displayed after the “square” button had been pushed?