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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?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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...
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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 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 NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
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?
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.
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?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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?
Charlie and Lynne 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?
A Sudoku with clues as ratios or fractions.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
How many different symmetrical shapes can you make by shading triangles or squares?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.
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.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
A Sudoku with clues as ratios.
A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?
Use the differences to find the solution to this Sudoku.
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.
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. . . .
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Given the products of adjacent cells, can you complete this Sudoku?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
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?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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?"
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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?
Label this plum tree graph to make it totally magic!
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 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.
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
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?