Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
What is the best way to shunt these carriages so that each train
can continue its journey?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
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.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
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?
A Sudoku with clues given as sums of entries.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
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.
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many different triangles can you make on a circular pegboard that has nine pegs?
Find out what a "fault-free" rectangle is and try to make some of
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
Use the clues to colour each square.
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
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?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
How many different rhythms can you make by putting two drums on the
What is the least number of moves you can take to rearrange the
bears so that no bear is next to a bear of the same colour?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
How many triangles can you make on the 3 by 3 pegboard?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?