List

Number Operations and Calculation Methods - Short Problems

Split clock face
problem

Split clock face

Age
11 to 14
Challenge level
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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.
Reverse Subtraction
problem

Reverse subtraction

Age
11 to 14
Challenge level
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What is the value of c in this subtraction?
Missing Digits
problem

Missing digits

Age
11 to 14
Challenge level
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Can you find the missing digits in this calculation?
Fly Away
problem

Fly away

Age
11 to 14
Challenge level
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Can you work out the values of the digits in this addition sum?
Hot Dogs
problem

Hot dogs

Age
11 to 14
Challenge level
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How many hot dogs did this hot dog lover eat on the first day of her binge?
Identical digit multiplication
problem

Identical digit multiplication

Age
11 to 14
Challenge level
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77 is multiplied by another two-digit number with identical digits. What is the product?
Bus Route
problem

Bus route

Age
11 to 14
Challenge level
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How far apart are the first and last bus stops in this bus route?
Debasing the Coinage
problem

Debasing the coinage

Age
11 to 14
Challenge level
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How much lighter will £5 worth of 5p's be with these new lighter coins?
Carry Over
problem

Carry over

Age
11 to 14
Challenge level
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Each letter stands for a different digit, and S is non-zero. Which letter has the lowest value?
2014 even numbers
problem

2014 even numbers

Age
11 to 14
Challenge level
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What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?
In Sum-mary
problem

In sum-mary

Age
11 to 14
Challenge level
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What does the sum of these three numbers tell us about their product?
Magic Error
problem

Magic error

Age
11 to 14
Challenge level
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Two of the numbers in a 4x4 magic square have been swapped. Can you work out the sum of these numbers?
Subtracting to 2008
problem

Subtracting to 2008

Age
11 to 14
Challenge level
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Can you work out the sum of the missing digits in this subtraction?
Down and Along
problem

Down and along

Age
11 to 14
Challenge level
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Can you work out the values of J, M and C in this sum?
354972
problem

354972

Age
11 to 14
Challenge level
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What is the remainder when 354972 is divided by 7?
50, 50, 50 and 50
problem

50, 50, 50 and 50

Age
11 to 14
Challenge level
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Aroon says his age is 50 years, 50 months, 50 weeks and 50 days. What age will he be on his next birthday?
Walk or Run?
problem

Walk or run?

Age
11 to 14
Challenge level
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Can you work out how long it will take for John to walk to and from school?
Sum of Ten
problem

Sum of ten

Age
11 to 14
Challenge level
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The sum of ten distinct positive integers is 100. What is the largest possible value of one of the numbers?
Quiz Question
problem

Quiz question

Age
11 to 14
Challenge level
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Can you work out how many quizzes have to be played before we have a winner?
Whole Numbers Only
problem

Whole numbers only

Age
11 to 14
Challenge level
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Can you work out how many of each kind of pencil this student bought?
Anti-Magic Square
problem

Anti-magic square

Age
11 to 14
Challenge level
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You may have met Magic Squares, now meet an Anti-Magic Square. Its properties are slightly different - can you still solve it?
Palindromic milometer
problem

Palindromic milometer

Age
11 to 14
Challenge level
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At the beginning and end of Alan's journey, his milometer showed a palindromic number. Can you find his maximum possible average speed?
So Many Sums
problem

So many sums

Age
11 to 14
Challenge level
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In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?
Multiple choice
problem

Multiple choice

Age
11 to 14
Challenge level
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How many questions did Sarah answer correctly in this multiple choice exam?
Currency Exchange
problem

Currency exchange

Age
11 to 14
Challenge level
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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.
Placeholder: several colourful numbers
problem

See axes

Age
11 to 14
Challenge level
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Which digit does X represent in this column sum?
Kangaroo Subtraction
problem

Kangaroo subtraction

Age
11 to 14
Challenge level
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Can you solve this 'KANGAROO' alphanumeric subtraction?
Placeholder: several colourful numbers
problem

ABC addition

Age
11 to 14
Challenge level
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Can you work out what a, b and c are in this sum?

Rolling Along the Trail
problem

Rolling along the trail

Age
11 to 14
Challenge level
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What could be the scores from five throws of this dice?
Placeholder: several colourful numbers
problem

Roses and carnations

Age
11 to 14
Challenge level
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How many different bunches of flowers can this class buy for their teacher?
Jam and Egg Sandwich
problem

Jam and egg sandwich

Age
11 to 14
Challenge level
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How many solutions can you find to this sum? Each of the different letters stands for a different number.
Operational Decision
problem

Operational decision

Age
11 to 14
Challenge level
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What symbol should be inserted to make the equation true?
Product and Sum
problem

Product and sum

Age
11 to 14
Challenge level
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When Jim rolled some dice, the scores had the same product and sum. How many dice did Jim roll?
Latin Multiplication
problem

Latin multiplication

Age
11 to 14
Challenge level
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Can you choose one number from each row and column in this grid to form the largest possibe product?
Birthday Tables
problem

Birthday tables

Age
11 to 14
Challenge level
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How many tables of each type does Mark need at his birthday party?
Filling Morecambe Bay
problem

Filling Morecambe Bay

Age
11 to 14
Challenge level
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"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?

Bookshop
problem

Bookshop

Age
11 to 14
Challenge level
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If Clara spends £23 on books and magazines, how many of each does she buy?
Squares and Cubes
problem

Squares and cubes

Age
11 to 14
Challenge level
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How many positive two-digit numbers are there whose square and cube both end in the same digit?
last digit
problem

Last digit

Age
11 to 14
Challenge level
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What is the last digit in this calculation involving powers?
Sum One Special
problem

Sum one special

Age
11 to 14
Challenge level
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Three different integers have a sum of 1 and a product of 36 - what are they?
Digit Deletion
problem

Digit deletion

Age
11 to 14
Challenge level
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What is the largest number of digits that could be erased from this 1000-digit number, to get a surprising result?
Placeholder: several colourful numbers
problem

Divisible by 55

Age
11 to 14
Challenge level
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Choose the digits $a$ and $b$ so that this number is divisible by 55.
Sum of 1s
problem

Sum of 1s

Age
11 to 14
Challenge level
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Can you find the last 5 digits of this sum?
Comparing Totals
problem

Comparing totals

Age
11 to 14
Challenge level
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Can you work out the solution to this tricky summation problem?