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
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?
Find the sum of all three-digit numbers each of whose digits is
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?
What happens when you round these three-digit numbers to the nearest 100?
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?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
What happens when you round these numbers to the nearest whole number?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
An investigation that gives you the opportunity to make and justify
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
This activity involves rounding four-digit numbers to the nearest thousand.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Find out what a "fault-free" rectangle is and try to make some of
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 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.
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?
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?
How many centimetres of rope will I need to make another mat just
like the one I have here?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
This challenge asks you to imagine a snake coiling on itself.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?