Skip to main content

King's Maths School

Challenge 476: Adding and Subtracting

Two games with opposite goals that require similar thinking!

A good solution to these problems would give the correct numerical answers with an explanation of which operations are required.

A great solution to these problems would explain why it's not possible to use fewer operations.

(1)

On my screen is the letter "A".

There are two operations I can perform: copy what is currently on my screen to the clipboard, or paste what is on the clipboard to the screen.

For example, if I choose "copy", "paste", "copy", "paste", "paste", then my screen will show AAAAAA.

How many operations are required for my screen to show 27 "A"s?

How many operations are required for my screen to show 31 "A"s?

(2)

I have a bag of red counters. 

There are two operations I can perform: (a) replace a red counter with a blue counter, or (b) remove red counters equal to the number of blue counters.

For example, if I choose (a) (a) (a) (b) (b), there will be 3 blue counters and 9 fewer red counters than I started with.

If I start with 25 red counters, how many operations are required to remove them all?

If I start with 26 red counters, how many operations are required to remove them all?

Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.