The Starman's Math Index
These should be the last clues the majority of you need to solve this problem; and they include another change in the previous table: This time you're being supplied with a combination of answers to a set of questions that may or may not exist in your mind yet (and it should now be clear that there's more than only one question you must ask). This table shows you can definitely narrow down the combinations to fewer possibilities, depending upon the answers you receive; if you ask the right kind of questions:
|
Possible
Combinations
|
X
|
Y
|
Z
|
||||
|
1 |
T,
L, R
|
No
|
No
|
N/A
|
|||
|
2
|
L,
T, R
|
No
|
No
|
N/A
|
|||
|
3
|
T,
R, L
|
Yes
|
N/A
|
No
|
|||
|
4
|
L,
R, T
|
Yes
|
N/A
|
No
|
|||
|
5
|
R,
T, L
|
Yes/No
|
Yes
|
Yes
|
|||
|
6
|
R,
L, T
|
Yes/No
|
Yes
|
Yes
|
|||
|
Note:
This Table applies to only the first two out
of a total of three questions that must be asked ! | |||||||
In our first two
scenarios (combinations 1 or 2), you would receive two No
answers in a row. This means you'd already know that Z
was the Randomizer, so those yellow blocks are filled with "N/A"
to indicate no answer is necessary. Your last question, therefore,
would be designed to separate the liar from the truthteller
in chairs X or Y.
The next four scenarios are only slightly more complex: If the randomizer (in combinations 5 or 6) answers your first question with a "Yes," then you would ask Z the next question instead, since X might be the randomizer. If you get a Yes answer to that question, then X must be the Randomizer. If you get a No, then Y must be the Randomizer; in which case, you wouldn't need to ask Y any questions at all ("N/A").
However, if X answers with a No, you'd simply go ahead and ask Y the next question, just as we did in the first two scenarios, but a Yes answer to that question would then prove that X was was definitely the Randomizer. Thus, for all six situations, there are four possible combinations of answers to our first two questions: No-No, Yes-No, Yes-Yes or No-Yes; giving us certainty as to whom the Randomizer is! Your third question then, must be able to separate liars from truthtellers.
Now you know that you must design questions which will elicit the correct sequence of responses suggested in the Table above (or one similar to it). I'm not saying that there is only one correct set of questions, but if you normally think like a binary computer (using terms like black and white), you might want to step back and try a different approach!
OK, another major Hint: Think in terms of probability (instead of a single sure thing) when designing your questions for whomever X, Y or Z might be!
Still can't solve the problem, then click here for your Final Hint!