All except four of the nine numbers from 11 to 19 can be put in a single sequence “16, 18, 15, 12, 14” where each successive pair (such as 12 and 14, or 18 and 15) has highest common factor greater than 1. If you make the longest possible sequence like this using as many as possible of the nine numbers from 111 to 119, how many numbers will be left out?
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Junior Mathematical Challenge 1997 (1997)
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