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.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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 ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
How many different rectangles can you make using this set of rods?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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 Zargoes use almost the same alphabet as English. What does this birthday message say?
A Sudoku with a twist.
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
A Sudoku with clues as ratios.
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
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. . . .
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
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.
Two sudokus in one. Challenge yourself to make the necessary connections.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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.
What is the best way to shunt these carriages so that each train can continue its journey?
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
A Sudoku that uses transformations as supporting clues.
A Sudoku with clues as ratios.
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
The clues for this Sudoku are the product of the numbers in adjacent squares.
A Sudoku with clues as ratios or fractions.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.