In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This article for primary teachers suggests ways in which to help children become better at working systematically.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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....?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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 package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
If you put three beads onto a tens/ones abacus you could make the
numbers 3, 30, 12 or 21. What numbers can be made with six beads?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A challenging activity focusing on finding all possible ways of stacking rods.
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
How many different triangles can you make on a circular pegboard that has nine pegs?
This challenge extends the Plants investigation so now four or more children are involved.
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.
Can you replace the letters with numbers? Is there only one
solution in each case?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you find all the different triangles on these peg boards, and
find their angles?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Find out what a "fault-free" rectangle is and try to make some of
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.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
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.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you substitute numbers for the letters in these sums?
Number problems at primary level that require careful consideration.
Can you find all the different ways of lining up these Cuisenaire
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?