This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Can you use the information to find out which cards I have used?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Choose a symbol to put into the number sentence.
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
If you have only four weights, where could you place them in order
to balance this equaliser?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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 5 darts and your target score is 44. How many different
ways could you score 44?
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!
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Can you hang weights in the right place to make the equaliser
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Find all the numbers that can be made by adding the dots on two dice.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
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.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Ben has five coins in his pocket. How much money might he have?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?