Brain strain

OK, hand up who's brain is in gear? Here's the answer to last week's Truth/Lie question.

There are 6 possible states for the order of the men: TRL, TLR, LTR, LRT, RTL, RLT, where T=truth teller, R=Random and L=Liar.

There are 8 possible combinations of anwers for questions: TTT, TTL, TLT, TLL, LTT, LTL, LLT, LLL, where T=Truth and L=Lie

Ask #1 if L is standing on R's right arm (our left if they are facing us).
The answer gives you a split in the order they are standing:
If YES, then it has to be T telling the truth, L telling a lie, or one of R's worthless answers, so: TLR, LTR, or RTL, RLT.
If NO, then it has to be T telling the truth, L telling a lie, or R and his worthless answers, so: TRL, LRT, or RTL, RLT.

Now we know, based on the answer to #1 where to avoid R's worthless answers. We now ask T or L "Is T in the lineup?" If answer 1 was Yes, we ask person 2, if it was no we ask person 3.

The answer now will give us some more info. If it's Yes, it's T answering the truth, if it's no, it's L answering a lie. So based on who we asked, we now know:

Yes, Yes: Has to be LTR, or RTL
Yes, No: TLR, RLT
No, Yes: LRT, RLT
No, No: TRL, RTL

Now any question separating the two possiblities works - just make sure you are avoiding R's worthless answers.

For example:
Yes, Yes - ask #2 if #1 is L. (We know #2 is T and will tell the truth) - Yes = LTR, No = RTL
Yes, No, - ask #2 if #1 is T. ( We know #2 is L and will tell a lie) - Yes = RLT, No = TLR
No, Yes - ask # 3 if #1 is L. (We know #3 is T and will tell the truth) - Yes = LRT, No = RLT
No, No, - ask #3 if #1 is T. (We know #3 is L and will tell a lie) - Yes = RTL, No = TRL

I think I'll give you a respite this week, so how about something a bit simpler?

We all know some latin. A good example is with numbers. We know Uni means one, dual means two, and tri means three. So, I'm going to give you some things that need words for them. I'll give 2 examples first...

• Billion = Million² or ^ 2 , Trillion = Million³ or ^ 3. So what is a million ^ 7?
• A triangle has 3 sides, a Pentagon has 5 sides. What would a 23 sided object be called?
• Binary is base 2, Decimal is base 10. What is base 32? (*ack*)
• United means as one. What about if it's split in two?
  
• A Bicycle has 2 wheels, a Trike has 3 wheels. What would a 4 wheeled bike be called?