Now and again I shall offer some interesting mathematical problems that my blog readers might like to solve – and perhaps use in the classroom, if they are teaching.

Here's a little mathematical problem that could be used with bright Year 6 pupils (10 to 11 years).

That's easy, of course. But I wondered how it would work if there was some kind of game of 29 rounds between 3 players (A, B and C), in which only one player can win each round. When would the match be over and one of the players declared the winner? Let's use

*a*,*b*and*c*for the numbers of rounds won so far by A, B and C.If

*a*= 12,*b*= 9 and*c*= 6, then A has won and the match is over. Why?But if

*a*= 11,*b*= 9 and*c*= 6, then no player is certain yet to win and the match must continue. Why?Can you find a general rule for when we can say that A has won? (Assume that A has the highest score and C the lowest).

You know what's coming next ... what about a rule for 4 players playing 29 rounds? 5 players?

Can you find a generalization for any number of players playing a game consisting of

*n*rounds?
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