# 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:

 Stage 3 ★ Sheet 1 Solutions Stage 3 ★★ Sheet 1 Solutions Sheet 2 Solutions Sheet 2 Solutions

### Magic Error

##### KS 3 Short Challenge Level:

Weekly Problem 12 - 2014
Two of the numbers in a 4x4 magic square have been swapped. Can you work out the sum of these numbers?

### Quiz Question

##### KS 3 Short Challenge Level:

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

### Carry Over

##### KS 3 Short Challenge Level:

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

### Hot-dogs

##### KS 3 Short Challenge Level:

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

### Operational Decision

##### KS 3 Short Challenge Level:

Weekly Problem 44 - 2014
What symbol should be inserted to make the equation true?

### Reverse Subtraction

##### KS 3 Short Challenge Level:

Weekly Problem 27 - 2006
What is the value of c in this subtraction?

### Identical Digit Multiplication

##### KS 3 Short Challenge Level:

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

### Subtracting to 2008

##### KS 3 Short Challenge Level:

Weekly Problem 2 - 2015
Can you work out the sum of the missing digits in this subtraction?

### Fly Away

##### KS 3 Short Challenge Level:

Weekly problem 50 - 2006
Can you work out the values of the digits in this addition sum?

### Down and Along

##### KS 3 Short Challenge Level:

Weekly Problem 50 - 2015
Can you work out the values of J, M and C in this sum?

### In Sum-mary

##### KS 3 Short Challenge Level:

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

### Filling Morecambe Bay

##### KS 3 Short Challenge Level:

Weekly Problem 19 - 2016
"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?

### Split Clock Face

##### KS 3 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.

### Walk or Run?

##### KS 3 Short Challenge Level:

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

### Bus Route

##### KS 3 Short Challenge Level:

Weekly Problem 17 - 2009
How far apart are the first and last bus stops in this bus route?

### 2014 Even Numbers

##### KS 3 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?

### 354972

##### KS 3 Short Challenge Level:

Weekly Problem 42 - 2016
What is the remainder when 354972 is divided by 7?

### Missing Digits

##### KS 3 Short Challenge Level:

Can you find the missing digits in this calculation?

### Sum of Ten

##### KS 3 Short Challenge Level:

The sum of 10 distinct positive integers is 100. What is the largest possible value of one of the numbers?

### Debasing the Coinage

##### KS 3 Short Challenge Level:

Weekly Problem 18 - 2009
How much lighter will £5 worth of 5p's be with these new lighter coins?

### 50, 50, 50 and 50

##### KS 3 Short Challenge Level:

Weekly Problem 16 - 2017
Aroon says his age is 50 years, 50 months, 50 weeks and 50 days old. What age will he be on his next birthday?

### Palindromic Milometer

##### KS 3 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?

##### KS 3 Short Challenge Level:

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

### Squares and Cubes

##### KS 3 Short Challenge Level:

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

### Kangaroo Subtraction

##### KS 3 Short Challenge Level:

Can you solve this 'KANGAROO' alphanumeric subtraction?

### Oldest and Youngest

##### KS 3 Short Challenge Level:

Weekly Problem 11 - 2017
Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?

### Digit Deletion

##### KS 3 Short Challenge Level:

Weekly Problem 14 - 2010
What is the largest number of digits that could be erased from this 1000-digit number, to get a surprising result?

### Sum of 1s

##### KS 3 Short Challenge Level:

Can you find the last 5 digits of this sum?

### Multiple Choice

##### KS 3 Short Challenge Level:

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

### Multiplication Mistake

##### KS 3 Short Challenge Level:

Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?

### Comparing Totals

##### KS 3 Short Challenge Level:

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

### So Many Sums

##### KS 3 Short Challenge Level:

Weekly Problem 20 - 2007
In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?

##### KS 3 Short Challenge Level:

What is the sum of these fractions?

### Rolling Along the Trail

##### KS 3 Short Challenge Level:

Weekly Problem 32 - 2011
What could be the scores from five throws of this dice?

### Jam and Egg Sandwich

##### KS 3 Short Challenge Level:

Weekly Problem 33 - 2011
How many solutions can you find to this sum? Each of the different letters stands for a different number.

### See Axes

##### KS 3 Short Challenge Level:

Which digit does X represent in this column sum?

### Bookshop

##### KS 3 Short Challenge Level:

Weekly Problem 3 - 2017
Books cost £3.40 and magazines cost £1.60. If Clara spends £23 on books and Magazines, how many of each does she buy?

### Last Digit

##### KS 3 Short Challenge Level:

What is the last digit in this calculation involving powers?