# Number Operations and Calculation Methods - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Number Operations and Calculation Methods.

Printable worksheets containing selections of these problems are available here.

### Carry Over

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

Each letter stands for a different digit, and S is non-zero. Which letter has the lowest value?

### 2014 Even Numbers

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

What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?

### Reverse Subtraction

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

What is the value of c in this subtraction?

### Missing Digits

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

Can you find the missing digits in this calculation?

### Magic Error

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

Two of the numbers in a 4x4 magic square have been swapped. Can you work out the sum of these numbers?

### Walk or Run?

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

Can you work out how long it will take for John to walk to and from school?

### Fly Away

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

Can you work out the values of the digits in this addition sum?

### 354972

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

What is the remainder when 354972 is divided by 7?

### Hot Dogs

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

How many hot dogs did this hot dog lover eat on the first day of her binge?

### Subtracting to 2008

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

Can you work out the sum of the missing digits in this subtraction?

### 50, 50, 50 and 50

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

Aroon says his age is 50 years, 50 months, 50 weeks and 50 days. What age will he be on his next birthday?

### Identical Digit Multiplication

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

77 is multiplied by another two-digit number with identical digits. What is the product?

### In Sum-mary

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

What does the sum of these three numbers tell us about their product?

### Bus Route

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

How far apart are the first and last bus stops in this bus route?

### Debasing the Coinage

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

How much lighter will £5 worth of 5p's be with these new lighter coins?

### Down and Along

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

Can you work out the values of J, M and C in this sum?

### Split Clock Face

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

Use 2 straight lines to split the clock face into 3 parts so that the sums of the numbers in each of the parts are equal.

### Birthday Tables

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

How many tables of each type does Mark need at his birthday party?

### Currency Exchange

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

Dan and Ann have 9 and 8 coins respectively. What is the smallest number of coins they must swap so they end up with equal amounts of money.

### See Axes

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

Which digit does X represent in this column sum?

### Filling Morecambe Bay

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

"It would take 20 million years to fill Morecambe Bay from a bath tap". What does this imply is the approximate capacity of Morecambe Bay?

### Palindromic Milometer

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

At the beginning and end of Alan's journey, his milometer showed a palindromic number. Can you find his maximum possible average speed?

### Operational Decision

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

What symbol should be inserted to make the equation true?

### Sum of Ten

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

The sum of ten distinct positive integers is 100. What is the largest possible value of one of the numbers?

### Kangaroo Subtraction

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

Can you solve this 'KANGAROO' alphanumeric subtraction?

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

Can you work out what a, b and c are in this sum?

### Quiz Question

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

Can you work out how many quizzes have to be played before we have a winner?

### So Many Sums

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

In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?

### Product and Sum

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

When Jim rolled some dice, the scores had the same product and sum. How many dice did Jim roll?

### Product of Fractions

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

Find the product of these mixed numbers

### Bookshop

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

If Clara spends £23 on books and magazines, how many of each does she buy?

### Multiple Choice

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

How many questions did Sarah answer correctly in this multiple choice exam?

### Latin Multiplication

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

Can you choose one number from each row and column in this grid to form the largest possibe product?

### Rolling Along the Trail

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

What could be the scores from five throws of this dice?

### Roses and Carnations

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

How many different bunches of flowers can this class buy for their teacher?

### Adding Tricky Fractions

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

What is the sum of these fractions?

### Anti-magic Square

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

You may have met Magic Squares, now meet an Anti-Magic Square. Its properties are slightly different - can you still solve it?

### Jam and Egg Sandwich

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

How many solutions can you find to this sum? Each of the different letters stands for a different number.

### Comparing Totals

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

Can you work out the solution to this tricky summation problem?

### Sum One Special

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

Three different integers have a sum of 1 and a product of 36 - what are they?

### Digit Deletion

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

What is the largest number of digits that could be erased from this 1000-digit number, to get a surprising result?

### Divisible by 55

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

Choose the digits $a$ and $b$ so that this number is divisible by 55.

### Squares and Cubes

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

How many positive two-digit numbers are there whose square and cube both end in the same digit?

### Last Digit

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

What is the last digit in this calculation involving powers?

### Sum of 1s

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

Can you find the last 5 digits of this sum?