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?
Given the products of adjacent cells, can you complete this Sudoku?
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 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 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?"
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
A few extra challenges set by some young NRICH members.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
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?
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?
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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 Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
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.
A challenging activity focusing on finding all possible ways of stacking rods.
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.
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.
Can you coach your rowing eight to win?
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.
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.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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...
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
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?
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?