1. The answer is 9/500, or 1.8%. The problem can be set up algebraically. For each trip, there is a 100% chance that you will arrive in pod A, B, or C. Let X be the chance that you arrive in pod A, & since it is twice as likely that you will arrive in A than B, there is only half the chance that you will arrive in B than A. So B is 1/2 X. By the same reasoning, there is only 1/6 the chance you would arrive in C than A, so C is 1/6 X. The equation thus looks like this: 100 = X + 1/2X + 1/6X. X=60, so A = 60, B = 30, & C = 10. These numbers correspond to the % chances you would arrive in each pod.
The answer is found by multiplying these three percentages together (i.e. .3 x .1 x .6). There is only a 1.8% chance that you would arrive in these 3 pods in this particular order for your only 3 trips to Exray.
2. This problem can be easily solved by using a simple diagram:
A B C
T L L
L T L
L L T
Each L represents a liar, & each T represents the man telling the truth. These are the only three possible permutations for the scenario given. The second permutation is actually not possible, because both A & C's statements cannot both be lies, as A cannot be both guilty & innocent. The first possibility makes B guilty, & the last possibility makes A guilty, so there is a 50/50 chance that A or B is guilty, & C is definitely innocent.
3. The saying referred to goes something like "don't change horses while crossing a stream." The answer is HORSE, & the homophone referred to is HOARSE.
6. None of the above statements are definitely true. Most Fleeks may be Grobs, but the number of Fleeks in the entire Grob population may be very small. Even though most Grobs are Diors, there is not guarantee that any of the Grobs that are Diors also happen to be Fleeks.
8. The answer is MINOTAUR. The last statement that "I am entirely in LABYRINTH" refers to the Labyrinth in mythology that was built by Daedalus, & which the minotaur lived in until slain by Theseus. I warned you that this one was tricky!
9. FROWARD. Another good answer, found by a site visitor, is WAYWARD.
B M L I R
A O A L U
N O B L E
AMPLE is another correct answer that was found by a reader, AMBLE by another, GABLE by another, and MAPLE by yet another!
11. 0. For each square, multiply the number in the upper left hand corner by the number in the lower right hand corner, & then multiply the result by 3. The first digit of the answer is written in the lower left hand corner, & the second digit of the answer is in the upper right hand corner.
12. 1. For each square, the 2 bottom numbers are multiplied together, & the first digit (except for the third square, for which the first 2 digits are used) of the answer is written in the upper right hand corner, & the second digit is written in the upper left hand corner.