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Sunday Times Teaser 2182 – Team Bonding

by Ahmet Cetinbudaklar

The 21 members of a football squad, who wear the numbers 1 to 21, were asked to attend a training session but some were missing as a result of injuries. They were asked to stand in a circle in such a way that, for any adjacent players, one of their numbers was a multiple of the other.

It was then noticed that this was the largest number of players from the squad for which this was possible.  One player also noticed that the sum of the numbers of his immediate neighbours was equal to the lowest of the numbers among the missing players. A little further clockwise around the circle, another player found that the sum of the numbers of his immediate neighbours was equal to the highest number among the missing players. In no case did any player’s two immediate neighbours numbers add to 20.

Starting at player 1, list the numbers of players around the circle clockwise.

3 Comments Leave one →
  1. brian gladman permalink

  2. ahmet cetinbudaklar permalink

    Dear Brian

    You are so kind to? remind me of my teaser with a programming solution, one which I shall keep as a souvenir.

  3. Ogee permalink

    Players with prime numbers > 10 must be injured. I quickly found a loop for the remaining players, with 2 neighbours summing to the largest injury, but my first attempt didn’t have neighbours summing to the smallest. But there’s only one way to achieve that, so the change was easy, just swapping 2 adjacent players. A similar change creates or removes a 20 summation. I’m fairly sure that my final loop is unique.

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