Four of these clues are needed to find the chosen number on this
grid and four are true but do nothing to help in finding the
number. Can you sort out the clues and find the number?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
Who said that adding, subtracting, multiplying and dividing
couldn't be fun?
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
What is the sum of all the digits in all the integers from one to
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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
There are nasty versions of this dice game but we'll start with the nice ones...
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
Choose two digits and arrange them to make two double-digit
numbers. Now add your double-digit numbers. Now add your single
digit numbers. Divide your double-digit answer by your single-digit
answer. . . .
Explore the relationship between simple linear functions and their
When asked how old she was, the teacher replied: My age in years is
not prime but odd and when reversed and added to my age you have a
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
Think of any three-digit number. Repeat the digits. The 6-digit
number that you end up with is divisible by 91. Is this a
There are six numbers written in five different scripts. Can you sort out which is which?
Three people chose this as a favourite problem. It is the sort of
problem that needs thinking time - but once the connection is made
it gives access to many similar ideas.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
Can you substitute numbers for the letters in these sums?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
Find the sum of all three-digit numbers each of whose digits is
Take any four digit number. Move the first digit to the 'back of
the queue' and move the rest along. Now add your two numbers. What
properties do your answers always have?
Consider all two digit numbers (10, 11, . . . ,99). In writing down
all these numbers, which digits occur least often, and which occur
most often ? What about three digit numbers, four digit numbers. . . .
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 addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
Follow the clues to find the mystery number.
Consider all of the five digit numbers which we can form using only
the digits 2, 4, 6 and 8. If these numbers are arranged in
ascending order, what is the 512th number?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
A church hymn book contains 700 hymns. The numbers of the hymns are
displayed by combining special small single-digit boards. What is
the minimum number of small boards that is needed?
Carry out cyclic permutations of nine digit numbers containing the
digits from 1 to 9 (until you get back to the first number). Prove
that whatever number you choose, they will add to the same total.
The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?
What happens when you round these three-digit numbers to the nearest 100?