Equations and Formulae - Short Problems


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.


Partial Magic

Age 11 to 14 Short Challenge Level:

This magic square has only been partially completed. Can you still solve it...

Interstellar

Age 11 to 14 Short Challenge Level:

What number could replace * so that */5 is between 3 and 4?

Luis' Eight

Age 11 to 14 Short 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?

Shape Sums

Age 11 to 14 Short Challenge Level:

Given some relationships amongst these shapes, how many triangles equal one diamond?

Seven Dwarfs

Age 11 to 14 Short Challenge Level:

The Seven Dwarfs have seven different birthdays. How old can they be?

Five-to

Age 11 to 14 Short Challenge Level:

The number 2005 is the sum of a sequence of five consecutive positive integers. What is the smallest of these integers?

Star Sum

Age 11 to 14 Short Challenge Level:

You may have seen magic squares before, but can you work out the missing numbers on this magic star?

Multiplication Mistake

Age 11 to 14 Short Challenge Level:

Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?

Geometric Quadrilateral

Age 11 to 14 Short 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?

Fifty Coins

Age 11 to 14 Short Challenge Level:

Cheryl finds a bag of coins. Can you work out how many more 5p coins than 2p coins are in the bag?

Symbol

Age 11 to 14 Short Challenge Level:

Using the new operator $\oplus$, can you solve this equation?

Turnips

Age 11 to 14 Short Challenge Level:

Baldrick could buy 6 parsnips and 7 turnips, or 8 parsnips and 4 turnips. How many parsnips could he buy?

Crossover

Age 11 to 14 Short 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?

Magic 7

Age 11 to 14 Short Challenge Level:

Can you complete this magic square with the numbers from 7 to 15?

Named Products

Age 11 to 14 Short Challenge Level:

Can you find the solution to this equation? Each of the different letters stands for a different number.

To Run or Not to Run?

Age 11 to 14 Short 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?

Bat and Ball

Age 14 to 16 Short Challenge Level:

Can you work out how much this bat costs?

Weighing the Baby

Age 14 to 16 Short 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?

I Love Musical Stars

Age 14 to 16 Short Challenge Level:

Each row and column has the total given. What is the value of the heart symbol?

Table Total

Age 14 to 16 Short Challenge Level:

Can you find the sum of all of the numbers in the table?

Adjacent Additions

Age 14 to 16 Short 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?

Symmetric Reasoning

Age 14 to 16 Short Challenge Level:

Can you sum up the solutions to this equation?

In the Hundreds

Age 14 to 16 Short Challenge Level:

For how many positive values of $n$ are both $\frac n2$ and $2n$ three-digit whole numbers?

Pure Algebra

Age 14 to 16 Short Challenge Level:

Can you work out the product of $a$ and $b$ from the information in the question?

Big Fish

Age 14 to 16 Short 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...

Oldest and Youngest

Age 14 to 16 Short 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?

Sum = Product = Quotient

Age 14 to 16 Short Challenge Level:

Can you find a pair of numbers such that their sum, product and quotient are all equal? Are there any other pairs?

Traffic Tunnel

Age 14 to 16 Short Challenge Level:

Will these vehicles fit through this tunnel?

Simultaneous Multiplying

Age 14 to 16 Short 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 $a+b+c$?

Relative Angles

Age 14 to 16 Short Challenge Level:

Can you work out the angles of a triangle from the relationships between them?

Alien Currency

Age 14 to 16 Short 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?

Tennis Training

Age 14 to 16 Short Challenge Level:

After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?

Reciprocal Values

Age 14 to 16 Short Challenge Level:

Manipulate one algebraic fraction to solve another.

Monetary Difference

Age 14 to 16 Short Challenge Level:

Al, Bertie, Chris and Di have sums of money totalling £150... What is the difference between the amount Al and Di have?

Algebraic Differences

Age 14 to 16 Short Challenge Level:

If $6x−y=21$ and $6y−x=14$, what is the value of $x−y$?

Well Read

Age 14 to 16 Short 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?

Three Fruits

Age 14 to 16 Short Challenge Level:

Quince, quonce and quance are three types of fruit. Can you work out the order of heaviness of the fruits?

Day of the Triffids

Age 14 to 16 Short Challenge Level:

Jasmine buys three different types of plant. How many triffids did she buy?

Weighing Scales

Age 14 to 16 Short Challenge Level:

Can you work out how many spheres will balance a single pyramid?

Square to a Rectangle

Age 14 to 16 Short 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?

Fractions of Fractions

Age 14 to 16 Short 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?

Near 10

Age 14 to 16 Short Challenge Level:

10 must remain within easy reach...

Average Surroundings

Age 14 to 16 Short Challenge Level:

Can you work out Ali's age based on the diagram?

Black and White Socks

Age 14 to 16 Short 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?

Table Height

Age 14 to 16 Short Challenge Level:

A table has blocks of wood placed on and next to it. Can you work out how tall it is?

Packing Boxes

Age 14 to 16 Short 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.

Thousands of X

Age 14 to 16 Short Challenge Level:

Can you solve this scary-looking equation?

A Third of the Area

Age 14 to 16 Short Challenge Level:

The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?

Nested Square Roots

Age 14 to 16 Short Challenge Level:

Can you find the value of this expression, which contains infinitely nested square roots?