Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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?
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...
Different combinations of the weights available allow you to make different totals. Which totals can you make?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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.
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?"
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
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 mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
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?
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?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Given the products of adjacent cells, can you complete this Sudoku?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
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. . . .
Use the differences to find the solution to this Sudoku.
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.
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?
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.
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. . . .
This Sudoku, based on differences. Using the one clue number can you find the solution?
A few extra challenges set by some young NRICH members.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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.
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.
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?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Find out about Magic Squares in this article written for students. Why are they magic?!
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
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?
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 letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
A challenging activity focusing on finding all possible ways of stacking rods.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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?
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.