A Sudoku with clues given as sums of entries.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
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 Sudoku that uses transformations as supporting clues.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A Sudoku with a twist.
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
Two sudokus in one. Challenge yourself to make the necessary
The puzzle can be solved with the help of small clue-numbers which
are either placed on the border lines between selected pairs of
neighbouring squares of the grid or placed after slash marks on. . . .
A Sudoku with clues as ratios.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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.
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 in them?
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.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
A Sudoku with clues as ratios or fractions.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Given the products of diagonally opposite cells - can you complete this Sudoku?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
This challenge extends the Plants investigation so now four or more children are involved.
How many models can you find which obey these rules?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
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 few extra challenges set by some young NRICH members.
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
A challenging activity focusing on finding all possible ways of stacking rods.
Can you find all the different triangles on these peg boards, and
find their angles?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
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?