Learning to Be Systematic

When you are working on a problem, do you approach it in a random and chaotic manner, or do you have a system to make sure you don't miss anything? This collection of problems has been chosen to demonstrate the power of a systematic approach, and we hope that as you work on the tasks you will take the time to develop efficient strategies for getting to a solution and recording what you have done.

Sticky Numbers and 1 Step, 2 Step include solutions that have previously been submitted to NRICH, so you may wish to try these problems first and then compare your approach with the published ones. Then try M, M and M and Counting Factors, and send us your solutions!

Sticky Numbers

Age 11 to 14 Challenge Level:

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

1 Step 2 Step

Age 11 to 14 Challenge Level:

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

M, M and M

Age 11 to 14 Challenge Level:

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Counting Factors

Age 11 to 14 Challenge Level:

Is there an efficient way to work out how many factors a large number has?