4 Sept 2013

No Sweets For You!: Lower Secondary Mathematics Competition Question

During a break, a class of 7 children sit in a circle around their teacher to play a game. The teacher has a bag of 12 sweets and wishes to hand them all out. Knowing that some children will get more than others, he has devised this game to distribute them 'fairly'. He walks clockwise close to the children and hands out the sweets to some of them according to the following rule. He selects one child and gives him a sweet, then he skips the next child and gives a sweet to the next one, then he skips 2 and gives a sweet to the next one, then he skips 3, and so on.

After he has handed out all the sweets, the children look bemused - the game hasn't really worked very well! How many of the children end up with no sweets at all?

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