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.

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.

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?

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?

ABC Addition

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.

Birthday Tables

Age 11 to 14 Short Challenge Level:

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

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?

Comparing Totals

Age 11 to 14 Short Challenge Level:

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