Enigma 1481: No calculator, please!
27 November 2012
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From New Scientist #2643, 16th February 2008
I had 10 different cards, each bearing one of the digits 0 to 9 (6 was distinguishable from 9). I selected six cards with consecutive digits and formed three two-digit numbers. I wrote down a number which was not 1 but was a factor of each of the three two-digit numbers. I multiplied the three two-digit numbers together and noticed that their product was odd. I found that the product had as a factor the cube of a number that was not 1 and was not the number I had written down.
Without any serious multiplications, tell me which three two-digit numbers I formed, in ascending order.