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Puzzle for Today

Puzzle No. 322 – Thursday 26 September

A row of around ten coins of various denominations are placed on a table. Justin and Steve take turns to take a coin from either end. They continue to do this until there are no coins left. Justin and Steve then add up the value of money they have collected. The winner is the person who has collected the most money. It is possible that you can always create a winning game by understanding a very simple mathematical concept. What maths do you need to know?

Today’s #PuzzleForToday has been set by Dr Steve Humble, Head of Education, Newcastle University

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Odd and even numbers.

The coins on the table are in a pattern of odd and even numbers. For example if you have nine coins in a row the odd number coins are 1, 3, 5, 7, 9. If Justin takes the first coin it has to be odd. Either 1 or 9. Therefore regardless of which coins Justin takes on future turns Steve can always select all the ‘even’ position coins. If these coins are the highest monetary value then Steve wins.

On the radio Steve used ten coins with coin one a 5p and coin ten a 1p to ‘force’ an ‘even coin’ winning strategy.

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