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5 

Troll Toll 
1 

Classic Knights & Knaves 
0 

Plane In The Wind 
How many?
Only one  the author of the puzzle context 
How many?
If the man, who author met, went in the same direction then the answer is 2753, since the sacks are not living creatures that could be going somewhere. context 
Troll Toll
2 context 
Troll Toll
2 context 
Psycho Killer
To meet the guy again at her sister's funeral context 
Sum of Two Prime Numbers
Never. Otherwise the would be a prime number between p and q. context 
Odd Pills
Take from the first jar 1 pill, 2 from the second, 3 from the third one,... 5 from fifth If the weight is 149, then ( 150  149 ) = 1 then the first jar contains 9 gram pills If the weight is 148, then ( 150  148 ) = 2 then the second jar contains 9 gram pills .... 145 means that the 5th jar has lightweighted pills context 
Multiples of 8 plus 1
Yes. (2n + 1)^2 = 4 n(n + 1) + 1 = [as n or n+1 is even => n(n+1) is even => n( n + 1) = 2m ] = 4 * 2m + 1 = 8m + 1 context 
Classic Knights & Knaves
1  Knight, 2  Knight, 3  Knave Suppose, the 1st one said "I am a Knight", but is a Knave Then the second said truth by saying "He said he is Knight", but lied when said "He is", that is contradiction to the condition "Knights always tell the truth, and Knaves always lie". In this case the first could not be neither the firsts, not the seconds. So the second inhabitant said truth and is a Knight. context 
Plane In The Wind
Increased. Solve the comparison: S / ( V1 + V2) + S / (V1  V2) and 2S / V1 , where V1  the plane speed, V2  the wind speed context 
3 Coins
75% 0.5 probability that the coin is onlyheads coin, and in this case we have 1 probability that it would heads next 0.5 probability that the coin is fair and in this case we have 0.5 probability that it would heads next. By the rule of condition probability, we have as a result: 0.5 * 1 + 0.5 * 0.5 = 0.75 context 