Students don't always know how to approach a problem systematically and often work in a random and chaotic manner. This collection of problems provides opportunities to discuss ways of organising and structuring ideas, and can be used to help draw attention to the benefits of working systematically.
Sticky Numbers and 1 Step, 2 Step include solutions that have previously been submitted to NRICH, so students may wish to try these problems first and then compare their own approaches with the published ones. Then they could go on to try M, M and M and Counting Factors, which are open for them to submit their own solutions.
problem
Favourite
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?
problem
Favourite
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?
problem
Favourite
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?
problem
Favourite
Counting Factors
Age
11 to 14
Challenge level
Is there an efficient way to work out how many factors a large number has?