This is part of our collection of Short Problems.
You may also be interested in our longer problems on Equations and Formulae Age 11-14 and Age 14-16.
Printable worksheets containing selections of these problems are available here.
problem
Five-to
Age
11 to 14
Challenge level
The number 2005 is the sum of a sequence of five consecutive positive integers. What is the smallest of these integers?
problem
Luis' eight
Age
11 to 14
Challenge level
Luis writes down eight consecutive positive integers. The sum of the three smallest numbers is 33. What is the sum of the three largest numbers?
problem
Shape sums
Age
11 to 14
Challenge level
Given some relationships amongst these shapes, how many triangles equal one diamond?
problem
Partial magic
Age
11 to 14
Challenge level
This magic square has only been partially completed. Can you still solve it...
problem
Interstellar
Age
11 to 14
Challenge level
What number could replace * so that */5 is between 3 and 4?
problem
Seven dwarfs
Age
11 to 14
Challenge level
The Seven Dwarfs have seven different birthdays. How old can they be?
problem
Symbol
Age
11 to 14
Challenge level
Using the new operator $\oplus$, can you solve this equation?
problem
Fifty coins
Age
11 to 14
Challenge level
Cheryl finds a bag of coins. Can you work out how many more 5p coins than 2p coins are in the bag?
problem
Crossover
Age
11 to 14
Challenge level
The numbers 2 to 8 are to be placed in the diagram so that the row and column each adds to 21. Which numbers can replace x?
problem
Geometric quadrilateral
Age
11 to 14
Challenge level
Each interior angle in a quadrilateral (apart from the smallest) is twice the previous one. What is the size of the smallest interior angle?
problem
Multiplication mistake
Age
11 to 14
Challenge level
Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?
problem
Turnips
Age
11 to 14
Challenge level
Baldrick could buy 6 parsnips and 7 turnips, or 8 parsnips and 4 turnips. How many parsnips could he buy?
problem
Star sum
Age
11 to 14
Challenge level
You may have seen magic squares before, but can you work out the missing numbers on this magic star?
problem
Named products
Age
11 to 14
Challenge level
Can you find the solution to this equation? Each of the different letters stands for a different number.
problem
Magic 7
Age
11 to 14
Challenge level
Can you complete this magic square with the numbers from 7 to 15?
problem
To run or not to run?
Age
11 to 14
Challenge level
If an athlete takes 10 minutes longer to walk, run and cycle three miles than he does to cycle all three miles, how long does it take him?
problem
Weighing the baby
Age
14 to 16
Challenge level
Weighing the baby at the clinic was a problem. Can you work out the total weight of the baby, the nurse and me from the information given?
problem
Adjacent additions
Age
14 to 16
Challenge level
In a 7-digit numerical code, each group of four consecutive digits adds to 16, and each group of five consecutive digits adds to 19. What is the sum of all 7 digits?
problem
In the hundreds
Age
14 to 16
Challenge level
For how many positive values of $n$ are both $\frac n2$ and $2n$ three-digit whole numbers?
problem
I love musical stars
Age
14 to 16
Challenge level
Each row and column has the total given. What is the value of the heart symbol?
problem
Table total
Age
14 to 16
Challenge level
Can you find the sum of all of the numbers in the table?
problem
Symmetric reasoning
Age
14 to 16
Challenge level
Can you sum up the solutions to this equation?
problem
Pure algebra
Age
14 to 16
Challenge level
Can you work out the product of $a$ and $b$ from the information in the question?
problem
Weighing scales
Age
14 to 16
Challenge level
Can you work out how many spheres will balance a single pyramid?
problem
Average surroundings
Age
14 to 16
Challenge level
Can you work out Ali's age based on the diagram?
problem
Sum = product = quotient
Age
14 to 16
Challenge level
Can you find a pair of numbers such that their sum, product and quotient are all equal? Are there any other pairs?
problem
Reciprocal values
Age
14 to 16
Challenge level
Manipulate one algebraic fraction to solve another.
problem
Packing boxes
Age
14 to 16
Challenge level
Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.
problem
Alien currency
Age
14 to 16
Challenge level
The planet Zog has both green and blue bank notes. Can you work out how many zogs two green and three blue bank notes are worth?
problem
Algebraic differences
Age
14 to 16
Challenge level
If $6x−y=21$ and $6y−x=14$, what is the value of $x−y$?
problem
Well read
Age
14 to 16
Challenge level
If you know how many books each boy, girl and teddy bear borrowed from the library, can you work out the number of girls?
problem
Oldest and youngest
Age
14 to 16
Challenge level
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?
problem
Tennis training
Age
14 to 16
Challenge level
After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?
problem
Relative angles
Age
14 to 16
Challenge level
Can you work out the angles of a triangle from the relationships between them?
problem
Square to a rectangle
Age
14 to 16
Challenge level
Kevin has moved some tiles to change the shape of his patio from a square to a rectangle. What are the lengths of the sides of the rectangle?
problem
Black and white socks
Age
14 to 16
Challenge level
There are 20 black socks and some white socks in a drawer. Can you work out how many of the socks are white?
problem
Day of the Triffids
Age
14 to 16
Challenge level
Jasmine buys three different types of plant. How many triffids did she buy?
problem
Fractions of fractions
Age
14 to 16
Challenge level
If you know that a fraction of X is the same as a different fraction of Y, can you work out X/Y?
problem
Table height
Age
14 to 16
Challenge level
A table has blocks of wood placed on and next to it. Can you work out how tall it is?
problem
Big fish
Age
14 to 16
Challenge level
Granny has taken up deep-sea fishing! Last week, she caught a fish so big that she had to cut it into three pieces in order to weigh it...
problem
Simultaneous multiplying
Age
14 to 16
Challenge level
If $a \times b=2$, $b \times c=24$, $c \times a=3$ and $a$, $b$ and $c$ are positive, what is the value of $a+b+c$?
problem
Monetary difference
Age
14 to 16
Challenge level
Al, Bertie, Chris and Di have sums of money totalling £150... What is the difference between the amount Al and Di have?
problem
Three fruits
Age
14 to 16
Challenge level
Quince, quonce and quance are three types of fruit. Can you work out the order of heaviness of the fruits?
problem
Nested square roots
Age
14 to 16
Challenge level
Can you find the value of this expression, which contains infinitely nested square roots?
problem
A third of the area
Age
14 to 16
Challenge level
The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?