Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
An investigation that gives you the opportunity to make and justify
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Find the sum of all three-digit numbers each of whose digits is
What happens when you round these three-digit numbers to the nearest 100?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Find out what a "fault-free" rectangle is and try to make some of
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
What happens when you round these numbers to the nearest whole number?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
How many centimetres of rope will I need to make another mat just
like the one I have here?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Got It game for an adult and child. How can you play so that you know you will always win?
How can you arrange these 10 matches in four piles so that when you
move one match from three of the piles into the fourth, you end up
with the same arrangement?
This activity involves rounding four-digit numbers to the nearest thousand.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
Delight your friends with this cunning trick! Can you explain how
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Can you dissect an equilateral triangle into 6 smaller ones? What
number of smaller equilateral triangles is it NOT possible to
dissect a larger equilateral triangle into?