You are Here: Home >< GCSEs

# Maths question regarding series

Announcements Posted on
Four hours left to win £100 of Amazon vouchers!! Don't miss out! Take our short survey to enter 24-10-2016
1. A code for transmitting binary signals at night is devised which assigns an ordered combination of red and blue flashes to each letter of the alphabet. Inorder to keep transmissions short, the shortest possible ‘strings’ of red and blue flashes are assigned first:

One red flash for A
One blue flash for B
Two red flashes for C
One red followed by one blue flash for D
And so on, introducing longer strings as necessary.

Given that flashes will be transmitted once a second and a one second gap will be left in
between letters, how many seconds would it take to transmit the entire alphabet of 26 letters?
A 82 seconds
B 85 seconds
C 98 seconds
D 107 seconds
E 123 seconds
2. sachinrahul

Write out the binary combinations for more letters and a pattern will emerge.
3. So you can think of them as like strings of 0s and 1s, red for 0 and blue for 1
Then choosing a code of a certain length, for instance, 2, amounts to choosing between 0 and 1 twice. I.e. you have two choices for the first digit and then, independently, two choices for the second digit, giving you 2*2 choices overall, so 4. It's easy enough to just write down the different choices here, 00, 01, 10, 11, but you can then apply the same principles to 3 digits and see how many strings of length 3 there are, and so on until there are enough strings to cover the alphabet.

(Original post by sachinrahul)
A code for transmitting binary signals at night is devised which assigns an ordered combination of red and blue flashes to each letter of the alphabet. Inorder to keep transmissions short, the shortest possible ‘strings’ of red and blue flashes are assigned first:

One red flash for A
One blue flash for B
Two red flashes for C
One red followed by one blue flash for D
And so on, introducing longer strings as necessary.

Given that flashes will be transmitted once a second and a one second gap will be left in
between letters, how many seconds would it take to transmit the entire alphabet of 26 letters?
A 82 seconds
B 85 seconds
C 98 seconds
D 107 seconds
E 123 seconds
4. (Original post by Kvothe the arcane)
sachinrahul

Write out the binary combinations for more letters and a pattern will emerge.

Thank you very much.
5. (Original post by 13 1 20 8 42)
So you can think of them as like strings of 0s and 1s, red for 0 and blue for 1
Then choosing a code of a certain length, for instance, 2, amounts to choosing between 0 and 1 twice. I.e. you have two choices for the first digit and then, independently, two choices for the second digit, giving you 2*2 choices overall, so 4. It's easy enough to just write down the different choices here, 00, 01, 10, 11, but you can then apply the same principles to 3 digits and see how many strings of length 3 there are, and so on until there are enough strings to cover the alphabet.

Thank you very much.

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: May 12, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### Who is getting a uni offer this half term?

Find out which unis are hot off the mark here

Poll
Useful resources

## Study tools

### Essay expert

Learn to write like a pro with our ultimate essay guide.

See where you can apply with our uni match tool

### Make study resources

Create all the resources you need to get the grades.

### Create your own Study Plan

Organise all your homework and exams so you never miss another deadline.

### Resources by subject

From flashcards to mind maps; there's everything you need for all of your GCSE subjects.

### Find past papers

100s of GCSE past papers for all your subjects at your fingertips.