# Equations and Formulae Stage 4 - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Equations and Formulae - Stage 4.

Printable worksheets containing selections of these problems are available here:

 Stage 4 ★ Sheet 1 Solutions Sheet 2 Solutions Sheet 3 Solutions

### Named Products

##### KS 4 Short Challenge Level:

Weekly Problem 42 - 2010
Can you find the solution to this equation? Each of the different letters stands for a different number.

### Square to a Rectangle

##### KS 4 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?

### I Love Musical Stars

##### KS 4 Short Challenge Level:

Weekly Problem 42 - 2015
Each row and column has the total given. What is the value of the heart symbol?

### Near 10

##### KS 4 Short Challenge Level:

Weekly Problem 4 - 2011
10 must remain within easy reach...

### Big Fish

##### KS 4 Short Challenge Level:

Weekly Problem 21 - 2007
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...

### Table Total

##### KS 4 Short Challenge Level:

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

### Weighing the Baby

##### KS 4 Short Challenge Level:

Weekly Problem 2 - 2014
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?

### Weighing Scales

##### KS 4 Short Challenge Level:

Weekly Problem 35 - 2008
A child's box of bricks contains cubes, cones and spheres. Can you work out how many spheres will balance a single cone?

### Symmetric Reasoning

##### KS 4 Short Challenge Level:

Can you sum up the solutions to this equation?

### Algebraic Differences

##### KS 4 Short Challenge Level:

Weekly Problem 42 - 2014
If $6x−y=21$ and $6y−x=14$, what is the value of $x−y$?

### Sum = Product = Quotient

##### KS 4 Short Challenge Level:

Weekly Problem 15 - 2010
Can you find a pair of numbers such that their sum, product and quotient are all equal? Are there any other pairs?

### Pure Algebra

##### KS 4 Short Challenge Level:

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

### Interstellar

##### KS 4 Short Challenge Level:

Weekly Problem 22 - 2012
What number could replace * so that */5 is between 3 and 4?

##### KS 4 Short Challenge Level:

Weekly Problem 3 - 2015
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?

### Bat and Ball

##### KS 4 Short Challenge Level:

Can you work out how much this bat costs?

### Day of the Triffids

##### KS 4 Short Challenge Level:

Weekly Problem 23 - 2013
Jasmine buys three different types of plant. How many triffids did she buy?

### In the Hundreds

##### KS 4 Short Challenge Level:

Weekly Problem 21 - 2015
For how many positive values of $n$ are both $\frac n2$ and $2n$ three-digit whole numbers?

### Table Height

##### KS 4 Short Challenge Level:

Weekly Problem 21 - 2006
A table has blocks of wood placed on and next to it. Can you work out how tall it is?

### Black and White Socks

##### KS 4 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?

##### KS 4 Short Challenge Level:

Weekly Problem 48 - 2015
Miss Quaffley's class went to the library. If you know how many books each boy, girl and teddy bear took out, can you work out how many girls there are?

### Months and Years

##### KS 4 Short Challenge Level:

Weekly Problem 1 - 2013
The product of Mary's age at her last birthday and her age in complete months is 1800. How old is Mary?

### Traffic Tunnel

##### KS 4 Short Challenge Level:

Will these vehicles fit through this tunnel?

### Simultaneous Multiplying

##### KS 4 Short Challenge Level:

Weekly Problem 17 - 2007
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 $a+b+c$?

### Unequal Statements

##### KS 4 Short Challenge Level:

Weekly Problem 32 - 2010
For what numbers are each of these statements true? How many of the statements can be true at the same time?