We have chosen a selection of our favourite NRICH resources that challenge you to work systematically.
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Here are a few questions you might need to ask along the way:
Which piece of information is the most useful to start with? What next?
How will I record my findings?
Will I be confident that I have found all the results by the end?
The problems can be tackled in any order.
![Two and Two](/sites/default/files/styles/medium/public/thumbnails/content-01-06-six2-icon.png?itok=r2AsNoHS)
problem
Two and Two
How many solutions can you find to this sum? Each of the different letters stands for a different number.
![1 Step 2 Step](/sites/default/files/styles/medium/public/thumbnails/content-00-10-penta1-icon.png?itok=wey3aDMe)
problem
1 Step 2 Step
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?
![ACE, TWO, THREE...](/sites/default/files/styles/medium/public/thumbnails/content-id-5775-icon.png?itok=fWWWcW02)
problem
ACE, TWO, THREE...
Can you picture how to order the cards to reproduce Charlie's card trick for yourself?
![Isosceles Triangles](/sites/default/files/styles/medium/public/thumbnails/content-id-2666-icon.png?itok=wmpakUQq)
problem
Isosceles Triangles
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
![m, m and m](/sites/default/files/styles/medium/public/thumbnails/content-id-6267-icon.png?itok=Q1S8r2JO)
problem
m, m and m
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
![Can they be equal?](/sites/default/files/styles/medium/public/thumbnails/content-id-6398-icon.png?itok=MaCLt6SR)
problem
Can they be equal?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
![Sticky Numbers](/sites/default/files/styles/medium/public/thumbnails/content-id-6571-icon.jpg?itok=gK-R2-2J)
problem
Sticky Numbers
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
![Shifting Times Tables](/sites/default/files/styles/medium/public/thumbnails/content-id-6713-icon.png?itok=y_Wtw3Cv)
problem
Shifting Times Tables
Can you find a way to identify times tables after they have been shifted up or down?
![Charlie's delightful machine](/sites/default/files/styles/medium/public/thumbnails/content-id-7024-icon.png?itok=TnFInR1F)
problem
Charlie's delightful machine
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
![American Billions](/sites/default/files/styles/medium/public/thumbnails/content-01-09-six5-icon.png?itok=jytZpqxV)
problem
American Billions
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...