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?

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

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.

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?

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

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?

Given the products of diagonally opposite cells - can you complete this Sudoku?

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?

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

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

A few extra challenges set by some young NRICH members.

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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?

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

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

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.

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?

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

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

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

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.

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.

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

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Can you use the information to find out which cards I have used?

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

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

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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

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

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.

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.

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

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.

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.

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?

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

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

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?

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