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.
problem
Two and Two
Age
7 to 16
Challenge level
How many solutions can you find to this sum? Each of the different letters stands for a different number.
problem
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
ACE, TWO, THREE...
Age
11 to 14
Challenge level
Can you picture how to order the cards to reproduce Charlie's card trick for yourself?
problem
Isosceles Triangles
Age
11 to 14
Challenge level
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?
problem
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
Can they be equal?
Age
11 to 14
Challenge level
Can you find rectangles where the value of the area is the same as the value of the perimeter?
problem
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
Shifting Times Tables
Age
11 to 14
Challenge level
Can you find a way to identify times tables after they have been shifted up or down?
problem
Charlie's delightful machine
Age
11 to 16
Challenge level
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
problem
American Billions
Age
11 to 14
Challenge level
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...