Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
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 merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Can you find the chosen number from the grid using the clues?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
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.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
Can you replace the letters with numbers? Is there only one solution in each case?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
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?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Can you work out some different ways to balance this equation?
This activity focuses on rounding to the nearest 10.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
What two-digit numbers can you make with these two dice? What can't you make?
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Have a go at balancing this equation. Can you find different ways of doing it?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
Number problems at primary level that require careful consideration.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.