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?

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

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

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

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

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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?

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

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.

Use the differences to find the solution to 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...

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

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?

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

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?

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?

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

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

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

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

How many different symmetrical shapes can you make by shading triangles or squares?

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.

A few extra challenges set by some young NRICH members.

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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.

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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.

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.

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.

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

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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

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

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

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

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

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 article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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

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?

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

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.

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

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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

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