# Resources tagged with: Place value

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Broad Topics > Numbers and the Number System > Place value ### 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. . . . ### 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... ### 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? ### Chocolate Maths

##### Age 11 to 14 Challenge Level:

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. . . . ### 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? ### The Number Jumbler

##### Age 7 to 14 Challenge Level:

The Number Jumbler can always work out your chosen symbol. Can you work out how? ### 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. ### Quick Times

##### Age 11 to 14 Challenge Level:

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible. ### 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. . . . ### 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)? ##### 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 ### 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"? ### Football Sum

##### Age 11 to 14 Challenge Level:

Find the values of the nine letters in the sum: FOOT + BALL = GAME ### Digit Sum

##### Age 11 to 14 Challenge Level:

What is the sum of all the digits in all the integers from one to one million? ### Eleven

##### Age 11 to 14 Challenge Level:

Replace each letter with a digit to make this addition correct. ##### Age 11 to 14 Challenge Level:

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true. ### Cycle It

##### Age 11 to 14 Challenge Level:

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. ### 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? ### Even Up

##### Age 11 to 14 Challenge Level:

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? ### Song Book

##### Age 7 to 11 Challenge Level:

A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit cards. What is the minimum number of small cards that is needed? ### 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? ##### Age 5 to 11 Challenge Level:

Who said that adding couldn't be fun? ### 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? ### Double Digit

##### Age 11 to 14 Challenge Level: ### Subtraction Surprise

##### Age 7 to 14 Challenge Level:

Try out some calculations. Are you surprised by the results? ### Skeleton

##### Age 11 to 14 Challenge Level:

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum. ### Not a Polite Question

##### Age 11 to 14 Challenge Level:

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 perfect square... ### 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? ### Trebling

##### Age 7 to 11 Challenge Level:

Can you replace the letters with numbers? Is there only one solution in each case? ### What Do You Need?

##### Age 7 to 11 Challenge Level:

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? ### 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" . ### Basically

##### Age 11 to 14 Challenge Level:

The number 3723(in base 10) is written as 123 in another base. What is that base? ### Six Times Five

##### Age 11 to 14 Challenge Level:

How many six digit numbers are there which DO NOT contain a 5? ### Back to the Planet of Vuvv

##### Age 11 to 14 Challenge Level:

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of. . . . ### 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? ### Pupils' Recording or Pupils Recording

##### Age 5 to 14

This article, written for teachers, looks at the different kinds of recordings encountered in Primary Mathematics lessons and the importance of not jumping to conclusions! ### 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. ##### 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? ### Being Resilient - Primary Number

##### Age 5 to 11 Challenge Level:

Number problems at primary level that may require resilience. ### Coded Hundred Square

##### Age 7 to 11 Challenge Level:

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up? ### Becky's Number Plumber

##### Age 7 to 11 Challenge Level:

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? ### Six Is the Sum

##### Age 7 to 11 Challenge Level:

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros? ### Calculator Bingo

##### Age 7 to 11 Challenge Level:

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. ### Multiply Multiples 2

##### Age 7 to 11 Challenge Level:

Can you work out some different ways to balance this equation? ### ABC

##### Age 7 to 11 Challenge Level:

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication? ### Multiply Multiples 1

##### Age 7 to 11 Challenge Level:

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it? ### Round the Dice Decimals 2

##### Age 7 to 11 Challenge Level:

What happens when you round these numbers to the nearest whole number? ### Round the Three Dice

##### Age 7 to 11 Challenge Level:

What happens when you round these three-digit numbers to the nearest 100? ### Round the Dice Decimals 1

##### Age 7 to 11 Challenge Level:

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number? ### Multiply Multiples 3

##### Age 7 to 11 Challenge Level:

Have a go at balancing this equation. Can you find different ways of doing it?