# 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. ### 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? ### 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? ### 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? ### 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? ##### 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? ### 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? ### 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. ##### 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? ### 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? ### 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? ### 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 $x−y$? ##### 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? ### 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?