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 car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
What is the sum of all the digits in all the integers from one to
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?
Replace each letter with a digit to make this addition correct.
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?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these numbers to the nearest whole number?
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 happens when you round these three-digit numbers to the nearest 100?
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?
There are six numbers written in five different scripts. Can you sort out which is which?
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?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
There are nasty versions of this dice game but we'll start with the nice ones...
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
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.
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
Find the sum of all three-digit numbers each of whose digits is
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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. . . .
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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 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?
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
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Can you work out some different ways to balance this equation?
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.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
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?
Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in
every possible order to give 5 digit numbers. Find the sum of the
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)?
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.
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?
How many six digit numbers are there which DO NOT contain a 5?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Follow the clues to find the mystery number.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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. . . .
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?