Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Follow the clues to find the mystery number.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you replace the letters with numbers? Is there only one
solution in each case?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
What could the half time scores have been in these Olympic hockey
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.
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
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 substitute numbers for the letters in these sums?
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....?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
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?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
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?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Given the products of adjacent cells, can you complete this Sudoku?
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?
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.
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?
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?
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
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.
Investigate the different ways you could split up these rooms so
that you have double the number.