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

Operational Decision

KS 3 Short Challenge Level:

Challenge Level:1

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

Reverse Subtraction

KS 3 Short Challenge Level:

Challenge Level:1

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

Identical Digit Multiplication

KS 3 Short Challenge Level:

Challenge Level:1

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

Subtracting to 2008

KS 3 Short Challenge Level:

Challenge Level:1

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

Fly Away

KS 3 Short Challenge Level:

Challenge Level:1

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:

Challenge Level:1

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:

Challenge Level:1

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

Filling Morecambe Bay

KS 3 Short Challenge Level:

Challenge Level:1

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:

Challenge Level:1

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:

Challenge Level:1

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

Bus Route

KS 3 Short Challenge Level:

Challenge Level:1

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:

Challenge Level:1

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:

Challenge Level:1

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

Missing Digits

KS 3 Short Challenge Level:

Challenge Level:1

Can you find the missing digits in this calculation?

Sum of Ten

KS 3 Short Challenge Level:

Challenge Level:1

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:

Challenge Level:1

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:

Challenge Level:1

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?

Magic Error

KS 3 Short Challenge Level:

Challenge Level:1

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:

Challenge Level:1

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

Carry Over

KS 3 Short Challenge Level:

Challenge Level:1

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:

Challenge Level:1

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

Squares and Cubes

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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:

Challenge Level:2 Challenge Level:2

Can you solve this 'KANGAROO' alphanumeric subtraction?

Oldest and Youngest

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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:

Challenge Level:2 Challenge Level:2

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:

Challenge Level:2 Challenge Level:2

Can you find the last 5 digits of this sum?

Multiple Choice

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Multiplication Mistake

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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:

Challenge Level:2 Challenge Level:2

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

So Many Sums

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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?

Adding Tricky Fractions

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

What is the sum of these fractions?

Rolling Along the Trail

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Jam and Egg Sandwich

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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:

Challenge Level:2 Challenge Level:2

Which digit does X represent in this column sum?

Palindromic Milometer

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

ABC Addition

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Last Digit

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the last digit in this calculation involving powers?

Bookshop

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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?