Enigma 1107: Factory work
10 July 2017
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From New Scientist #2263, 4th November 2000 [link]
When it comes to factor problems it is often quicker to use a bit of cunning logic than to resort to a computer or even a calculator, and here is one such puzzle.
Write down a four-figure number ending in 1 and then write down the next eight consecutive numbers, and then write down the nine numbers obtained by reversing the first nine. For example:
You could then count how many of all those numbers have a factor greater than 1 but less than 14: in this example there are actually eleven of them.
Your task now is to find a four-figure number ending in 1 so that, when you carry out this process, fewer than half the numbers have a factor greater than 1 but less than 14.
What is that four-figure number?