Thinking about solutions and solution methods - February 2011, Stage 4&5

This month we explore different ways of solving particular problems. Good problem solvers often reflect on their methods once they have constructed a solution. Is one method best? Most efficient? Most elegant? Would you use an alternative method of solution given the benefit of hindsight?

Problems

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Which Is Cheaper?

Stage: 4 Challenge Level: Challenge Level:1

When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?

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Which Is Bigger?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

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How Old Am I?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

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Weekly Challenge 22: Combinations of Two

Stage: 4 and 5 Short Challenge Level: Challenge Level:1

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

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A Long Time at the Till

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

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More Dicey Decisions

Stage: 5 Challenge Level: Challenge Level:1

The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?

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Interactive Workout - Further

Stage: 5 Challenge Level: Challenge Level:1

Give your further pure mathematics skills a workout with this interactive and reusable set of activities.