Thinking about solutions and solution methods - February 2011, All Stages

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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Cuisenaire Counting

Stage: 1 Challenge Level: Challenge Level:1

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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Largest Even

Stage: 1 Challenge Level: Challenge Level:1

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

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Rolling That Cube

Stage: 1 and 2 Challenge Level: Challenge Level:1

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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Curious Number

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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Chocolate

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

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Tea Cups

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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Inky Cube

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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Tilted Squares

Stage: 3 Challenge Level: Challenge Level:1

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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What Numbers Can We Make?

Stage: 3 Challenge Level: Challenge Level:1

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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Dozens

Stage: 3 Challenge Level: Challenge Level:1

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

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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.