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.
problem
In sum-mary
Age
11 to 14
Challenge level
What does the sum of these three numbers tell us about their product?
problem
Magic error
Age
11 to 14
Challenge level
Two of the numbers in a 4x4 magic square have been swapped. Can you work out the sum of these numbers?
problem
Subtracting to 2008
Age
11 to 14
Challenge level
Can you work out the sum of the missing digits in this subtraction?
problem
Down and along
Age
11 to 14
Challenge level
Can you work out the values of J, M and C in this sum?
problem
50, 50, 50 and 50
Age
11 to 14
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?
problem
Walk or run?
Age
11 to 14
Challenge level
Can you work out how long it will take for John to walk to and from school?
problem
Split clock face
Age
11 to 14
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.
problem
Reverse subtraction
Age
11 to 14
Challenge level
What is the value of c in this subtraction?
problem
Missing digits
Age
11 to 14
Challenge level
Can you find the missing digits in this calculation?
problem
Fly away
Age
11 to 14
Challenge level
Can you work out the values of the digits in this addition sum?
problem
Hot dogs
Age
11 to 14
Challenge level
How many hot dogs did this hot dog lover eat on the first day of her binge?
problem
Identical digit multiplication
Age
11 to 14
Challenge level
77 is multiplied by another two-digit number with identical digits. What is the product?
problem
Bus route
Age
11 to 14
Challenge level
How far apart are the first and last bus stops in this bus route?
problem
Debasing the coinage
Age
11 to 14
Challenge level
How much lighter will £5 worth of 5p's be with these new lighter coins?
problem
Carry over
Age
11 to 14
Challenge level
Each letter stands for a different digit, and S is non-zero. Which letter has the lowest value?
problem
2014 even numbers
Age
11 to 14
Challenge level
What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?
problem
Currency exchange
Age
11 to 14
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.
problem
Kangaroo subtraction
Age
11 to 14
Challenge level
Can you solve this 'KANGAROO' alphanumeric subtraction?
problem
Rolling along the trail
Age
11 to 14
Challenge level
What could be the scores from five throws of this dice?
problem
Roses and carnations
Age
11 to 14
Challenge level
How many different bunches of flowers can this class buy for their teacher?
problem
Jam and egg sandwich
Age
11 to 14
Challenge level
How many solutions can you find to this sum? Each of the different letters stands for a different number.
problem
Operational decision
Age
11 to 14
Challenge level
What symbol should be inserted to make the equation true?
problem
Product and sum
Age
11 to 14
Challenge level
When Jim rolled some dice, the scores had the same product and sum. How many dice did Jim roll?
problem
Latin multiplication
Age
11 to 14
Challenge level
Can you choose one number from each row and column in this grid to form the largest possibe product?
problem
Birthday tables
Age
11 to 14
Challenge level
How many tables of each type does Mark need at his birthday party?
problem
Filling Morecambe Bay
Age
11 to 14
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?
problem
Bookshop
Age
11 to 14
Challenge level
If Clara spends £23 on books and magazines, how many of each does she buy?
problem
Sum of ten
Age
11 to 14
Challenge level
The sum of ten distinct positive integers is 100. What is the largest possible value of one of the numbers?
problem
Quiz question
Age
11 to 14
Challenge level
Can you work out how many quizzes have to be played before we have a winner?
problem
Whole numbers only
Age
11 to 14
Challenge level
Can you work out how many of each kind of pencil this student bought?
problem
Anti-magic square
Age
11 to 14
Challenge level
You may have met Magic Squares, now meet an Anti-Magic Square. Its properties are slightly different - can you still solve it?
problem
Palindromic milometer
Age
11 to 14
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?
problem
So many sums
Age
11 to 14
Challenge level
In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?
problem
Multiple choice
Age
11 to 14
Challenge level
How many questions did Sarah answer correctly in this multiple choice exam?
problem
Digit deletion
Age
11 to 14
Challenge level
What is the largest number of digits that could be erased from this 1000-digit number, to get a surprising result?
problem
Divisible by 55
Age
11 to 14
Challenge level
Choose the digits $a$ and $b$ so that this number is divisible by 55.
problem
Comparing totals
Age
11 to 14
Challenge level
Can you work out the solution to this tricky summation problem?
problem
Squares and cubes
Age
11 to 14
Challenge level
How many positive two-digit numbers are there whose square and cube both end in the same digit?
problem
Last digit
Age
11 to 14
Challenge level
What is the last digit in this calculation involving powers?
problem
Sum one special
Age
11 to 14
Challenge level
Three different integers have a sum of 1 and a product of 36 - what are they?