Puzzle idea

[EvLer]

Main Question or Discussion Point

Hello everyone,
I was wondering if you could advise me a good puzzle I could give to my engineering-major friends, something tough that they would break their brains on . I was thinking of petals around the rose.
Any other suggestions are very much welcome!

 

[Tide]

How about this one?

What comes next in the sequence:

1
11
21
1211
111221
312211
...

?

It's guaranteed to bust their brain! :)

 

[EvLer]

Yeah...but I have to know the solution :surprised

ok, hold on, I'll try to bust my brains first, but I'm short on time...
edit: my solution: 13112221 correct?

 

[Tide]

EvLer,

Very good!

 

[JamesU]

Too easy. If you really want to stump 'em, give 'em this:

Three gods A , B , and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter.

Your task is to determine the identities of A , B , and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer in their own language, in which the words for yes and no are “da” and “ja”, in some order. You do not know which word means which.

and if you can memorize the answer:

Ask #1 "If uga = yes, then do those two [#2 and #3] always answer uga?"
If the answer is 'uga', then he's lying, because if uga really means yes, and #1 is the god of truth, then he will answer 'booga'. If 'uga'; means no, then the god of truth will still answer 'booga' because 'uga' does not mean yes. So if they answer 'booga' then they are telling the truth. That way you can make sure (depending on their answer) that they are for sure not the god of truth or for sure not the god of lying.

Ask #2 "Do the other two [#1 and #3] sometimes agree?"
The answer should be affirmative (whichever word that happens to be), if #2 is the god of truth, or no if it's the god of lying, unless #2 is the god who sometimes lies and sometimes tells the truth. If that's the case then you'll need the last question to clarify that.

Ask #3 "If uga = yes, then does that one [#1] always answer uga when the correct answer is uga?"
The answer again should be 'booga' if they are telling the truth, and 'uga' if they are lying. This time, however, if the answer is 'uga', then you know that this god is lying, and depending on the other answers you can find out which god is which:

A) - 'uga' - (lying god or chaos god)
B) - 'uga' - (lying god or chaos god because uga must mean yes in this case
C) - 'uga' - (truth god because the lying god won't answer correctly, and the chaos god won't always answer correctly)
#1=Liar #2=Chaos #3=Truth

A) - 'uga' - (lying god or chaos god)
B) - 'booga' - (chaos god or truth god)
C) - 'uga' - (chaos god or truth god), this set of answers only allows #1 to be the lying god, and #3 to be the truth god, thus #2 is the chaos god.
#1=Liar #2=Chaos #3=Truth

A) - 'booga' - (truth god or chaos god)
B) - 'booga' - (lying god or chaos god)
C) - 'uga' - (chaos god or lying god). This one is undetermined; but will most likely be:
#1=Truth #2=Lying #3=Chaos

A) - 'booga' - (truth god or chaos god)
B) - 'uga' - (chaos god or truth god)
C) - 'booga' - (lying god or chaos god). Again undetermined; but will most likely be:
#1=Truth #2=Chaos #3=Lying