Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Here is a chance to play a version of the classic Countdown Game.
Find out what a "fault-free" rectangle is and try to make some of your own.
Can you find all the different ways of lining up these Cuisenaire rods?
If you have only four weights, where could you place them in order to balance this equaliser?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
An environment which simulates working with Cuisenaire rods.
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you find all the different triangles on these peg boards, and find their angles?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Choose a symbol to put into the number sentence.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you complete this jigsaw of the multiplication square?
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
A card pairing game involving knowledge of simple ratio.
Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
A train building game for 2 players.
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Exchange the positions of the two sets of counters in the least possible number of moves