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Oh for the Mathematics of Yesteryear

A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45 days against the siege of the enemy?

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Tree Tops

A manager of a forestry company has to decide which trees to plant. What strategy for planting and felling would you recommend to the manager in order to maximise the profit?

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Thirty Nine, Seventy Five

We have exactly 100 coins. There are five different values of coins. We have decided to buy a piece of computer software for 39.75. We have the correct money, not a penny more, not a penny less! Can you discover what the five different types of coins are worth and how many of each we have saved?

Quick Ticket

Stage: 3 Short Challenge Level: Challenge Level:1


If I pay the exact fare, the smallest number of coins I could use is 4 (2 x 20p and 2 x 2p). If I receive change, then it is not possible for only 2 coins to change hands since this would involve my giving the driver one coin (50p, £1 or £2) and receiving only one coin in change, but the necessary coin does not exist. However, if I give the driver a 50p coin and receive a 5p coin and a 1p coin in change, then only 3 coins change hands.

This problem is taken from the UKMT Mathematical Challenges.