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.

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...

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...

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?

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?

Carry Over

KS 4 Short Challenge Level:

Weekly Problem 24 - 2009
Each letter stands for a different digit, and S is non-zero. Which letter has the lowest value?

Symmetric Reasoning

KS 4 Short Challenge Level:

Can you sum up the solutions to this equation?

Interstellar

KS 4 Short Challenge Level:

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

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?

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?

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?

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?

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?

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 $a+b+c$?

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?

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?

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?

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?