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 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?
A few extra challenges set by some young NRICH members.
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?
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.
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.
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. . . .
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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 NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
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?
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?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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...
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku with clues as ratios or fractions.
How many different symmetrical shapes can you make by shading triangles or squares?
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.
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
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.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
In this matching game, you have to decide how long different events take.
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
A Sudoku that uses transformations as supporting clues.
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?
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. . . .
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Two sudokus in one. Challenge yourself to make the necessary
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Find out what a "fault-free" rectangle is and try to make some of
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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