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 ...?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
How many different rectangles can you make using this set of rods?
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?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
How many possible necklaces can you find? And how do you know you've found them all?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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.
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.
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 your own double-sided magic square. But can you complete both sides once you've made the pieces?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
In this matching game, you have to decide how long different events take.
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.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
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.
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
What is the best way to shunt these carriages so that each train can continue its journey?
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?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
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 article for primary teachers suggests ways in which to help children become better at working systematically.
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.