Equations and Formulae Stage 3 - 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 3.

Printable worksheets containing selections of these problems are available here:

Stage 3 ★ Sheet 1 Solutions            Stage 3 ★★ Sheet 1 Solutions

Between a Square and a Cube

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 51 - 2011
The equation $x^2+2=y^3$ looks nearly quadratic. What integer solutions can you find?

Five-to

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 22 - 2015
The number 2005 is the sum of a sequence of five consecutive positive integers. What is the smallest of these integers?

Packing Boxes

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 28 - 2011
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.

Turnips

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 37 - 2012
Baldrick could buy 6 parsnips and 7 turnips, or 8 parsnips and 4 turnips. How many parsnips could he buy?

Debt Recovery

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 7 - 2009
Tony and Tina can't work out which of them owes what to the other. Can you?

Shape Sums

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 22 - 2016
Given some relationships amongst these shapes, how many triangles equal one diamond?

Average Surroundings

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 15 - 2009
Can you work out Ali's age based on the diagram?

Currency Exchange

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 48 - 2009
Dan and Ann have 9 and 8 coins respectively. What is the smallest number of coins they must swap so they end up with equal amounts of money.

Partial Magic

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 41 - 2011
This magic square has only been partially completed. Can you still solve it...

Fifty Coins

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 50 - 2014
Cheryl finds a bag of coins. Can you work out how many more 5p coins than 2p coins are in the bag?

Seven Dwarfs

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 13 - 2010
The Seven Dwarfs have seven different birthdays. How old can they be?

Tennis Training

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 40 - 2017
After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?

Symbol

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 2 - 2011
Using the new operator $\oplus$, can you solve this equation?

Geometric Quadrilateral

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 49 - 2017
Each interior angle in a quadrilateral (apart from the smallest) is twice the previous one. What is the size of the smallest interior angle?

Fractions of Fractions

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 44 - 2013
If you know that a fraction of X is the same as a different fraction of Y, can you work out X/Y?

Monetary Difference

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 50 - 2007
Al, Bertie, Chris and Di have sums of money totalling £150... What is the difference between the amount Al and Di have?

Alien Currency

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 22 - 2014
The planet Zog has both green and blue banknotes. Can you work out how many zogs two green banknotes and three blue banknotes are worth?

To Run or Not to Run?

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 38 - 2012
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?

Crossover

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 14 - 2017
The numbers 2 up to 8 are to be placed in the diagram on the right such that the row and column add up to 21. Which numbers can replace x?

Star Sum

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 40 - 2011
You may have seen magic squares before, but can you work out the missing numbers on this magic star?

Equal Means

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 36 - 2017
What value of x makes the mean of the first three numbers in this list equal to the mean of the other four?

Magic 7

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

Weekly Problem 36 - 2015
Can you complete this magic square with the numbers from 7 to 15?

Granny's Age

KS 3 & 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 10 - 2015
Granny is four times as old as I am. Five years ago she was five times as old as I was. What is the sum of our ages?

Square and Cube

KS 3 & 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 24 - 2014
The square of a positive number is twice as big as the cube of that number. What is the number?

Algebraic Differences

KS 4 Short Challenge Level:

Challenge Level:1

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