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(You may like to use this
to investigate this problem)
The situation : You have access to a communications link which you
share with other users.
The link sends a stream of data in pulses at set intervals - a
little like an escalator where each step carries a character.
The data you need to send comes in chunks of two different sizes -
a yellow chunk has $5$ characters and a blue chunk has $9$
Slots in the data stream become available and you have to decide if
you can use them efficiently with your yellow and blue data
For example a $180$ character slot could take $20$ blue
And a $78$ character slot could take $3$ yellow and $7$ blue
Slots come up very frequently so its only worth taking the ones you
can fill exactly.
For example a slot of size $31$ cannot be exactly filled with a
combination of yellow and blue chunks.
Begin by exploring what slot sizes near to $31$ can, or cannot, be
Don't rush that, but when you have a good feel for the problem move
on to generalise this situation.
Your two chunks are not necessarily lengths of $5$ or $9$
Whatever two lengths you choose there will be slot sizes you cannot
Investigate how the two chunk lengths determine the slot sizes that
will or will not work.
Describe your findings
You may find the Excel file Data Chunks useful.
If you spend a moment looking at the numbers you'll soon see how
this spreadsheet file works.
There is also something you should know about spreadsheets and
Using ICT is often brilliant for getting lots of results fast,
leaving your mind free to think about what's going on, but doing
some calculating yourself gives you an on-the-ground feel for the
So the trick is to use both approaches, getting the benefit from
The Data Chunks problem is a challenge.
It takes time and determination, but if you've enjoyed wrestling
with it then we feel confident that you'll want to see these links
There is an NRICH article by Alan and Toni Beardon about
Click for Part One
then there's a Part Two
to take you on further.
Another article, this time by Vicky Neale and Matthew Buckley is
Yet another by Vicky is called Introductory