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Challenge 253: Bob's Dance Club

Bob encourages people to attend his weekly dance club by bringing 60p and splitting it between the people who turn up. He always brings exactly 60p in coins and wants to be able to split it exactly between everyone else who turns up. However, he doesn’t want to be carrying a ton of change around all day, so wants to bring as few coins as possible.

a) On week 1, he knows Aiden, Mazie and Harriet will turn up, as they are his best friends and always want to support his dance club. Daniel is a lot less reliable, but he tries to come if he can. Bob knows nobody else will turn up (his dance club is not very popular, despite the incentives). What coins should he bring so he can split them exactly whether there are 3 or 4 members?

b) Bob is excited about his week 2 dance club, because as well as Aiden, Mazie, Harriet and Daniel, he has invited a new acquaintance, Debbie, to join. He doesn’t know Debbie very well, so she might or might not attend, and Daniel is still a bit unreliable. What coins should he bring so he can split it exactly if there are 3, 4 or 5 members?

c) Bob decides that too many coins are needed in parts a) and b) and decides to bring BobCoins instead. One BobPenny is equivalent to a regular penny, but he can create coins in whatever denominations he finds convenient. How does this change your answer to a) and b)?

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Please do send in your solution to this problem to  weeklymaths@kcl.ac.uk  You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide you with feedback on your solution.

 

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