How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
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.
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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.
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.
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
A challenging activity focusing on finding all possible ways of stacking rods.
Find out what a "fault-free" rectangle is and try to make some of
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
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?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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?
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.
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 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?
This challenge extends the Plants investigation so now four or more children are involved.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
A few extra challenges set by some young NRICH members.
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 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 package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
What happens when you round these numbers to the nearest whole number?
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. . . .
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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?