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?"
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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. . . .
Given the products of adjacent cells, can you complete this Sudoku?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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.
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.
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 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.
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?
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?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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.
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?
A few extra challenges set by some young NRICH members.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
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?
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?
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.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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.
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 tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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. . . .
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
A challenging activity focusing on finding all possible ways of stacking rods.
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
This challenge extends the Plants investigation so now four or more children are involved.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
A pair of Sudoku puzzles that together lead to a complete solution.
A Sudoku with clues as ratios.
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?
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.
Two sudokus in one. Challenge yourself to make the necessary
A Sudoku that uses transformations as supporting clues.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
The clues for this Sudoku are the product of the numbers in adjacent squares.
This Sudoku, based on differences. Using the one clue number can you find the solution?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
A Sudoku with clues given as sums of entries.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?