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.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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?
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
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 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?
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 nine.
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.
This challenge extends the Plants investigation so now four or more children are involved.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
A challenging activity focusing on finding all possible ways of stacking rods.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
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.
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?
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?"
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
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?
Given the products of adjacent cells, can you complete this Sudoku?
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.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
How many different symmetrical shapes can you make by shading triangles or squares?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Can you find all the different ways of lining up these Cuisenaire rods?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you find all the different triangles on these peg boards, and find their angles?
Number problems at primary level that require careful consideration.
Have a go at balancing this equation. Can you find different ways of doing it?
Can you replace the letters with numbers? Is there only one solution in each case?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?