Solution to Prime Number Upside down

Here are few:
3718103 = edibile
5355307 = loesses
5734051 = isohels
53517001 = idolises
55076051 = isogloss
55373603 = edgeless
77185181 = ibisbill
378163771 = illegible
537816173 = eligibles
3216070301 = ideologize
03216070301 = ideologized

Solution to The count puzzle

0 .. 1
1 .. 11
2 .. 2
3 .. 1
4 .. 1
5 .. 1
6 .. 1
7 .. 1
8 .. 1
9 .. 1

Solution to Lateral Thinking - The Elevator Puzzle

The man is a dwarf. He can't reach the upper elevator buttons, but he can ask people to push them for him. He can also push them with his umbrella.

Solution to Prisoner's Hat Puzzle

For the sake of explanation let's label the prisoners in line order A B and C. Thus B can see A (and A's hat colour) and C can see A and B.
The prisoners know that there are only two hats of each colour. So if C observes that A and B have hats of the same colour, C would deduce that his own hat is the opposite colour. However, if A and B have hats of different colours, then C can say nothing. The key is that prisoner B, after allowing an appropriate interval, and knowing what C would do, can deduce that if C says nothing the hats on A and B must be different. Being able to see A's hat he can deduce his own hat colour. (The fourth prisoner is irrelevant to the puzzle: his only purpose is to wear the fourth hat).
In common with many puzzles of this type, the solution relies on the assumption that all participants are totally rational and are intelligent enough to make the appropriate deductions.
After solving this puzzle, some insight into the nature of communication can be gained by pondering whether the meaningful silence of prisoner C violates the "No communication" rule (given that communication is usually defined as the "transfer of information").


Solution for the difficult form -:
In the case where every player has to make a guess, but they are free to choose when to guess, there is a strategy that allows every player to guess correctly. Each player should act as follows:
Count the numbers b of black hats and w of white hats.
Wait min(b,w) seconds.
If nobody has yet spoken, guess that your hat is black if you can see fewer black hats than white hats, or white if you can see fewer white hats than black hats.
If you have not yet spoken, guess that your hat is of the opposite colour to that of one of the first people to speak.
Suppose that in total there are B black hats and W white hats. There are three cases.
If B = W then those players wearing black hats see B−1 black hats and B white hats, so wait B−1 seconds then correctly guess that they are wearing a black hat. Similarly, those players wearing a white hat will wait W−1 seconds before guessing correctly that they are wearing a white hat. So all players make a correct guess at the same time.
If B < W then those wearing a black hat will see B−1 black hats and W white hats, whilst those wearing a white hat will see B black hats and W−1 white hats. Since B−1 < B ≤ W−1, those players wearing a black hat will be the first to speak, guessing correctly that their hat is black. The other players then guess correctly that their hat is white.
The case where W < B is similar.

Solution to Fork in the Road

A logician vacationing in the Bahamas finds himself on an island inhabited by two proverbial tribes of liars and truth-tellers. Members of one tribe always speak the truth, while other always lie. He stands at the fork of a road (a Tee-junction) and has to ask a bystander which leg he needs to follow to reach the village. He knows not whether the native is a truth-teller or a liar. The logician thinks for a moment and then asks only one question. What does he ask?


Another solution- Pick a road and ask, “Will the other guy tell me that this is the right road to take to get to town?” If it’s the right road and you ask the truth teller, he’ll know that the liar will say no, and thus say no. If you ask the liar, he’ll know that the truth teller would says yes, so he’ll lie and say no. If the road was the wrong road to take, the truth teller will know that the liar would says yes, and thus say yes. If you ask the liar, he’ll know that the truth teller would say no, so he’ll lie and say yes.

Solution to Licence To Kill

1)The first bit is easy, as the first letter of each plate spells WHODUNNIT IX
(A challenge to our Inspector.)

2)The second bit is a little trickier, If you read the last three letters in each plate from the bottom up and right to left you get
ADVANCE EACH LETTER BY THE NUMBER SHOWN, so advance W by 5 to get B,
H by 13 to get U and so on until you spell BUTLER DID IT

Solution to Match and Lemon-aid Puzzle

First, the waiter stuck the match into the lemon wedge, so that it would stand straight. Then he lit the match, and put it in the middle of the plate with the lemon. Then, he placed the glass upside-down over the match. As the flame used up the oxygen in the glass, it created a small vacuum, which sucked in the water through the space between the glass and the plate. Thus, the waiter got the water into the glass without touching or moving the plate.