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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
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?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Use the differences to find the solution to this Sudoku.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
Four small numbers give the clue to the contents of the four
Label this plum tree graph to make it totally magic!
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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 particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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.
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 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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
The clues for this Sudoku are the product of the numbers in adjacent squares.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
A pair of Sudoku puzzles that together lead to a complete solution.
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.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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 pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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.
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...
A Sudoku with a twist.
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.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Given the products of adjacent cells, can you complete this Sudoku?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
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.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
This Sudoku combines all four arithmetic operations.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Two sudokus in one. Challenge yourself to make the necessary
Each clue number in this sudoku is the product of the two numbers in adjacent cells.