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
Use the clues to colour each square.
A Sudoku with clues given as sums of entries.
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?
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?
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
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
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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?
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.
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?
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?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
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?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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 triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many different triangles can you make on a circular pegboard
that has nine pegs?
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?
Find out what a "fault-free" rectangle is and try to make some of
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 work out how to balance this equaliser? You can put more
than one weight on a hook.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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 trains can you make which are the same length as Matt's,
using rods that are identical?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
How many different rhythms can you make by putting two drums on the
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the
clues to work out which name goes with each face.
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?