This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Can you use the information to find out which cards I have used?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
Try this matching game which will help you recognise different ways of saying the same time interval.
In this matching game, you have to decide how long different events take.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Find out what a "fault-free" rectangle is and try to make some of your own.
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
My coat has three buttons. How many ways can you find to do up all the buttons?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
Can you find out in which order the children are standing in this line?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
Can you find all the different triangles on these peg boards, and find their angles?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?