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...
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
How many solutions can you find to this sum? Each of the different letters stands for a different 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?
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?
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.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?"
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
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.
Use the differences to find the solution to this Sudoku.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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.
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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 have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Four small numbers give the clue to the contents of the four
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
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?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A pair of Sudoku puzzles that together lead to a complete solution.