Find the sum of all three-digit numbers each of whose digits is
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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.
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
This activity involves rounding four-digit numbers to the nearest thousand.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
This activity focuses on rounding to the nearest 10.
This challenge is about finding the difference between numbers which have the same tens digit.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Got It game for an adult and child. How can you play so that you know you will always win?
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
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.
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?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
What happens when you round these numbers to the nearest whole number?
This challenge asks you to imagine a snake coiling on itself.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Are these statements always true, sometimes true or never true?
Stop the Clock game for an adult and child. How can you make sure you always win 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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
What happens when you round these three-digit numbers to the nearest 100?