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.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
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...
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.
The clues for this Sudoku are the product of the numbers in
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?
Use the differences to find the solution to this Sudoku.
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?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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 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
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 pair of Sudoku puzzles that together lead to a complete solution.
Given the products of diagonally opposite cells - can you complete
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?
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.
If you are given the mean, median and mode of five positive whole
numbers, can you find the numbers?
How many different symmetrical shapes can you make by shading triangles or squares?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
This Sudoku, based on differences. Using the one clue number can you find the solution?
Four small numbers give the clue to the contents of the four
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
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. . . .
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.
Given the products of adjacent cells, can you complete this Sudoku?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?"
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?
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.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Label this plum tree graph to make it totally magic!
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
Four friends must cross a bridge. How can they all cross it in just
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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.
A Sudoku with clues given as sums of entries.
Solve the equations to identify the clue numbers in this Sudoku problem.
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. . . .
Find out about Magic Squares in this article written for students. Why are they magic?!