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.

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

This challenge extends the Plants investigation so now four or more children are involved.

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.

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?

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?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

Use the differences to find the solution to this Sudoku.

A Sudoku that uses transformations as supporting clues.

Two sudokus in one. Challenge yourself to make the necessary connections.

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.

Four small numbers give the clue to the contents of the four surrounding cells.

A pair of Sudoku puzzles that together lead to a complete solution.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

Given the products of adjacent cells, can you complete this Sudoku?

A few extra challenges set by some young NRICH members.

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 Sudoku, based on differences. Using the one clue number can you find the solution?

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

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?

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

Two sudokus in one. Challenge yourself to make the necessary connections.

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

A challenging activity focusing on finding all possible ways of stacking rods.

Use the clues about the shaded areas to help solve this sudoku

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

You need to find the values of the stars before you can apply normal Sudoku rules.

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...

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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.

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!

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?

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.

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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 monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?