The Value of Working Systematically

The value of working systematically

Mathematicians often talk about the importance of working systematically on a problem, rather than approaching it in a random, unstructured way. The tasks in this feature have been chosen because systematic approaches will offer the most efficient routes to the solutions.

How Old Am I? 

Stage: 4 Challenge Level: Challenge Level:1
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?

Odds and Evens Made Fair 

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2
In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

Sorted 

Stage: 5 Challenge Level: Challenge Level:1
How can you quickly sort a suit of cards in order from Ace to King?

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?