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Maths question regarding series Watch

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.

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Updated: May 12, 2016
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