Thinking about solutions and solution methods - February 2011, Stage 3&4

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

Chocolate

Stage: 2 and 3 Challenge Level:

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?

Tea Cups

Stage: 2 and 3 Challenge Level:

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.

Inky Cube

Stage: 2 and 3 Challenge Level:

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?

Tilted Squares

Stage: 3 Challenge Level:

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

What Numbers Can We Make?

Stage: 3 Challenge Level:

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

Dozens

Stage: 3 Challenge Level:

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

Which Is Cheaper?

Stage: 4 Challenge Level:

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

How Old Am I?

Stage: 4 Challenge Level:

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?

Which Is Bigger?

Stage: 4 Challenge Level:

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

Weekly Challenge 22: Combinations of Two

Stage: 4 and 5 Short Challenge Level:

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

A Long Time at the Till

Stage: 4 and 5 Challenge Level:

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?