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# 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

### Interstellar

### Luis' Eight

### Shape Sums

### Seven Dwarfs

### Five-to

### Star Sum

### Multiplication Mistake

### Geometric Quadrilateral

### Fifty Coins

### Symbol

### Turnips

### Crossover

### Magic 7

### Named Products

### To Run or Not to Run?

### Weighing the Baby

### I Love Musical Stars

### Table Total

### Adjacent Additions

### Symmetric Reasoning

### In the Hundreds

### Pure Algebra

### Oldest and Youngest

### Sum = Product = Quotient

### Simultaneous Multiplying

### Relative Angles

### Alien Currency

### Tennis Training

### Reciprocal Values

### Monetary Difference

### Algebraic Differences

### Well Read

### Three Fruits

### Day of the Triffids

### Weighing Scales

### Square to a Rectangle

### Fractions of Fractions

### Average Surroundings

### Black and White Socks

### Table Height

### Packing Boxes

### Big Fish

### A Third of the Area

### Nested Square Roots

Or search by topic

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.

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

Can you sum up the solutions to this equation?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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 $a+b+c$?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

Manipulate one algebraic fraction to solve another.

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

If you know that a fraction of X is the same as a different fraction of Y, can you work out X/Y?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

There are 20 black socks and some white socks in a drawer. Can you work out how many of the socks are white?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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.

Age 14 to 16

ShortChallenge 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...

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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