Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
What happens when you round these three-digit numbers to the nearest 100?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
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!
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
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?
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?
Can you replace the letters with numbers? Is there only one solution in each case?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
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....?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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!
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Number problems at primary level that require careful consideration.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
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?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
In how many ways can you stack these rods, following the rules?
A challenging activity focusing on finding all possible ways of stacking rods.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
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?
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?