Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
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.
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.
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
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?
There are nasty versions of this dice game but we'll start with the nice ones...
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Who said that adding, subtracting, multiplying and dividing
couldn't be fun?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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 work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
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.
What is the sum of all the digits in all the integers from one to
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
Explore the relationship between simple linear functions and their
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
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.
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
There are six numbers written in five different scripts. Can you sort out which is which?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
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?
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?
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?
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?
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.
Find the sum of all three-digit numbers each of whose digits is
Follow the clues to find the mystery number.
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" .
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?
What happens when you round these three-digit numbers to the nearest 100?
This activity involves rounding four-digit numbers to the nearest thousand.
The number 3723(in base 10) is written as 123 in another base. What
is that base?
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten.
Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
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.
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. . . .
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)?