Solution to SGC Maths Quest 2: Play the game

St George’s College, Weybridge invited children from Years 5 and 6 at all local schools to take part in the second instalment of the SGC Maths Quest challenge.

Each Half Term, St George’s College will provide a Maths problem for children from Years 5 and 6 to solve. All correct entries will be displayed on the St George’s Weybridge website at www.stgeorgesweybridge.com

Solution to SGC Maths Quest 2: Play the game

There was another good response to this problem, with Dr Grant receiving many answers.

Well done to Monty Nendick, from Claremont Fan Prep School and Matthew Thompson at St Nicholas Church of England School, Shepperton, who solved the puzzle.

Here is Matthew’s reasoning on how to win the game:

"The way to win the game is to start by picking one counter if you go first. If the other player then takes only one you then take two. But if he takes two then take one. That should leave three and you should win.

If you go second, there is not a winning strategy if the first person knows the strategy. But you can win if the first person takes two, then you take two.

Your aim is to leave three in the middle when it is your opponents turn. Then you should win."

Dr Grant commented on the puzzle, saying:

"Well done both for figuring this out! This is a basic form of the ancient game of Nim. If you play with more than seven counters, you should always aim to leave your opponent with a number of counters that is a multiple of three. Because you are always picking one or two counters, you can continue to “force” your opponent to continue to always be left with multiples of three. If they pick one, you pick two (total of three). If they pick two, you pick one (multiple of three), and hence you will always be able to grab the last counter."

Well done again to all those who took part and particularly to Matthew and Monty who got the correct solution.

Please watch out for SGC Maths Quest 3, which will be published on 20 February 2017.

Here is the original problem:

To solve this problem, you will need seven objects, such as counters or blocks. It is a game for two players.

Place the 7 counters in a pile and decide who will go first. (In the next game, the other player will have the first turn.) Each player takes turns to take away either one or two counters.

The player who takes the last counter wins.

Keep playing until you work out a winning strategy.

Does it matter who has the first turn?

What happens when you start the game with more counters?

Download the full maths quest here

6 January 2017

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