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Виктория Яцкова

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3 Coins

75% 0.5 probability that the coin is only-heads 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

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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

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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.

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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

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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 light-weighted pills

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Sum of Two Prime Numbers

Never. Otherwise the would be a prime number between p and q.

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Psycho Killer

To meet the guy again at her sister's funeral

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Troll Toll

2

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Troll Toll

2

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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.

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How many?

Only one - the author of the puzzle

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