# 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

### 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?

### More Dicey Decisions

##### Stage: 5 Challenge Level:

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

### Interactive Workout - Further

##### Stage: 5 Challenge Level:

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