The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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?
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.
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.
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Find out what a "fault-free" rectangle is and try to make some of your own.
You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous 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?
A few extra challenges set by some young NRICH members.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Can you find all the different triangles on these peg boards, and find their angles?
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.
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?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
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?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?