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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?

Currency Exchange

Stage: 3 Short Challenge Level: Challenge Level:1

In total, Ann and Dan have 180p +  400p = 580p, so they need to end up with 290p each. Therefore Dan needs to receive at least three five pound coins from Ann to have enough money. Then, Ann has 250p, so she needs at least two two-pound coins from Dan, at which point they have £290p each. Therefore, at least 5 coins must change hands.

This problem is taken from the UKMT Mathematical Challenges.