Other tags that relate to A Biggy
Indices. Generalising. Place value. Multiplication & division. Prime numbers. Factors and multiples. Mathematical reasoning & proof. Creating and manipulating expressions and formulae. Divisibility. Working systematically.There are 64 results
Broad Topics > The Number System and Place Value > Place value
Just Repeat
Age 11 to 14
Challenge Level
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 coincidence?
Three Times Seven
Age 11 to 14
Challenge Level
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Multiplication Magic
Age 14 to 16
Challenge Level
Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .
Really Mr. Bond
Age 14 to 16
Challenge Level
115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?
Big Powers
Age 11 to 16
Challenge Level
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.
What a Joke
Age 14 to 16
Challenge Level
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
Repeaters
Age 11 to 14
Challenge Level
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.
Legs Eleven
Age 11 to 14
Challenge Level
Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
Please Explain
Age 11 to 14
Challenge Level
Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .
Exploring Simple Mappings
Age 11 to 14
Challenge Level
Explore the relationship between simple linear functions and their graphs.
Double Digit
Age 11 to 14
Challenge Level
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. . . .
What an Odd Fact(or)
Age 11 to 14
Challenge Level
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?
Novemberish
Age 14 to 16
Challenge Level
a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.
Read This Page
Age 11 to 14
Challenge Level
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Arrange the Digits
Age 11 to 14
Challenge Level
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?
Digit Sum
Age 14 to 16 Short
Challenge Level
What is the sum of all the digits in all the integers from one to one million?
Football Sum
Age 11 to 14
Challenge Level
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Enriching Experience
Age 14 to 16
Challenge Level
Find the five distinct digits N, R, I, C and H in the following nomogram
Cayley
Age 11 to 14
Challenge Level
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Phew I'm Factored
Age 14 to 16
Challenge Level
Explore the factors of the numbers which are written as 10101 in different number bases. Prove that the numbers 10201, 11011 and 10101 are composite in any base.
Diagonal Sums
Age 7 to 14
Challenge Level
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?
Add to 200
Age 11 to 14
Challenge Level
By selecting digits for an addition grid, what targets can you make?
Writ Large
Age 11 to 14
Challenge Level
Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.
Forwards Add Backwards
Age 11 to 14
Challenge Level
What happens when you add a three digit number to its reverse?
Subtraction Surprise
Age 7 to 14
Challenge Level
Try out some calculations. Are you surprised by the results?
Mini-max
Age 11 to 14
Challenge Level
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. . . .
Lesser Digits
Age 11 to 14
Challenge Level
How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?
Two and Two
Age 11 to 16
Challenge Level
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Tis Unique
Age 11 to 14
Challenge Level
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 possibility.
Method in Multiplying Madness?
Age 7 to 14
Challenge Level
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
X Marks the Spot
Age 11 to 14
Challenge Level
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" .
Number Rules - OK
Age 14 to 16
Challenge Level
Can you produce convincing arguments that a selection of statements about numbers are true?
DOTS Division
Age 14 to 16
Challenge Level
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
Latin Numbers
Age 14 to 16
Challenge Level
Can you create a Latin Square from multiples of a six digit number?
The Number Jumbler
Age 7 to 14
Challenge Level
The Number Jumbler can always work out your chosen symbol. Can you work out how?
Always a Multiple?
Age 11 to 14
Challenge Level
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Adding with the Abacus
Age 5 to 16
Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?
2-digit Square
Age 14 to 16
Challenge Level
A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?
Nice or Nasty for Two
Age 7 to 14
Challenge Level
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Alphabet Soup
Age 11 to 14
Challenge Level
This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.
Reversals
Age 11 to 14
Challenge Level
Where should you start, if you want to finish back where you started?
Nice or Nasty
Age 7 to 14
Challenge Level
There are nasty versions of this dice game but we'll start with the nice ones...
Plus Minus
Age 14 to 16
Challenge Level
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
Reach 100
Age 7 to 14
Challenge Level
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.
How Many Miles to Go?
Age 11 to 14
Challenge Level
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
Seven Up
Age 11 to 14
Challenge Level
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)?
Think of Two Numbers
Age 11 to 14
Challenge Level
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
More Mathematical Mysteries
Age 11 to 14
Challenge Level
Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .
NRICH is part of the family of activities in the Millennium Mathematics Project.