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?

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.

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?"

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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

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...

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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?

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.

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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?

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

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

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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?

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?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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.

The clues for this Sudoku are the product of the numbers in adjacent squares.

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?

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

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.

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

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.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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?

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

Find out about Magic Squares in this article written for students. Why are they magic?!

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.

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

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?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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?

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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?

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?

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

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ 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!

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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.