Riddles Round 3

[Firemeboy]

I thought about starting a Riddles Round 4 thread, and then starting with a 'where is round 3?' puzzle...  But I didn't.  Obviously.

Ok, enough shenanigans.

During the Cold War, a submarine communications officer received the following message in morse code which, when decoded, read:

TOP SECRET
Captain Brown
We have a spy in our midst and we believe he
is giving information to the Russians. We
have recently made a breakthrough and have
been able to narrow down our list of suspects
to one of the 252 members of your crew. We
have no exact information and no physical
description. We are convinced that you are
not the spy and as such we entrust you to
perform some covert investigation to aid us
in our attempt to catch the rogue operator.
We wish you good luck in this endeavour but
we must remind you to keep this secret. We
needn't remind you a refusal to follow these
instructions exactly to the letter will
result in an immediate courtmarshall.
Instructions for arrest:
1) If you fail to find the spy then, upon
docking you will ensure that none of your
crew can leave the ship.
2) If you do ascertain who the spy is then
you should arrest him, confine to the Brig
immediately & place him under 24 hour guard.
From this point on you should cease all
communications with us.

Naturally the Captain was purturbed by this message. He was just about to destroy the message to ensure safety when he was presented with another message which read.

Addendum to previous message:
D-C / T-H / A-A / O-H / C-A / X-K / W-A / O-F / X-D.

After the Captain read this message he was a little less purturbed than he was before and soon decided on an appropriate course of action. What was it?

[Eric James Stone]

The captain realized his communications officer had gone insane, so he locked him up?

Interesting puzzle.  I shall have to think more deeply.

[Firemeboy]

 Yeah, this is a fun one when you finally get it.  

[Tink]

Are they initials of those who have gotten this message before Captain Brown and who then sent it on to a new person? If so, he probably picked someone and sent it on to them with his initials added to the end of the list.

[Firemeboy]

Nope, not initials.

[Firemeboy]

Maybe it's time for a hint?

Count the number of lines in the message.

[Eric James Stone]

The second message decodes to:
Arrest your communications operator immediately he is the spy

[Firemeboy]

Correct.  Nicely done.

For the record, if anybody is wondering, I didn't make that puzzle up.  I didn't want to say before that I got it off the internet, or somebody would have gone and googled it.

EJS is up.

[Tink]

But I don't get how it translates. Sorry for being dumb, but can you explain, please?

[Eric James Stone]

The clue about the number of lines was what pushed me in the right direction.

There are 26 lines in the first message.  Assign a letter to each line in reverse alphabetic order.  (I tried normal order first, and it didn't work.)

In each letter pair in the second message, the first letter corresponds to a line of the message.  The second letter indicates a word on that line (A = 1st word, B = 2nd word, etc.)

And now, the next puzzle:

There's a room with 100 light bulbs with corresponding switches, numbered from 1 to 100.  All of the bulbs are off.

Outside the room are 100 people, numbered 1 to 100.

Person #1 enters the room and flips every switch from #1 to #100, thus turning on every bulb.

Person #2 then enters the room and flips switch #2 and every switch with a number that's a multiple of 2, thus turning those bulbs off.

Person #3 then enters the room and flips switch #3 and every switch with a number that's a multiple of 3, thus switching the state of those bulbs from off to on or vice versa.

Persons #4 to #100 follow the same procedure, each one flipping the switch for their number and all multiples of their number.

When they are all done, what is the state of bulb #64?  And how many bulbs are on?

[Lightning Eater]

Isn't that just a matter of making a big diagram in word, or am I missing something?

I'm assuming there's some kind of pattern, but I'm just making a big diagram on word.


Edit: ok, found the pattern, a total of ten lights will be on, including light no. 64

[Archon]

You can also do it mathematically Lightning. 64 would be flipped by all the factors of it, that is to say 1, 2, 4, 8, 16, 32, and 64. So it would be flipped a total of 7 times, which would mean that it is on. Then you figure that since all numbers with an odd number of factors are going to be on, and all the numbers with an even number are going to be on. Therefore, you can take out all the prime numbers, because they will be off. That's 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, and 89, right? Correct me if I am wrong, I just did that off the top of my head. If I am correct, then that is 25 lights off. I don't have time to continue my thought process right now, but I will post again when I do.

[Lightning Eater]

The pattern on my diagram was that they were all squares; 1,4,9,16,25,36,49,64,81,100

Edit: I'll admit though, that all I had noticed was that the difference was increasing by two each time, I only realised the square thing while typing them down just now, since I had never looked at them all together

[Firemeboy]

Very cool puzzle.

[Eric James Stone]

Lightning eater got it right.