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You walk up to a mountain that has two paths. One leads to the other side of the mountain, and the other will get you lost forever. Two twins know the path that leads to the other side. You can ask them only one question. Except! One lies and one tells the truth, and you don’t know which is which. So, What do you ask?
Answer: You ask each twin What would your brother say?. This works because.... Well let's say the correct path is on the left side. So say you asked the liar "What would your brother say?" Well, the liar would know his brother was honest and he would say the left side, but since the liar lies, he would say right. If you asked the honest twin the same question, he would say right, because he knows his brother will lie. Therefore, you would know that the correct path was the left!
Solution:
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You ask each twin What would your brother say?. This works because…. Well let’s say the correct path is on the left side. So say you asked the liar “What would your brother say?” Well, the liar would know his brother was honest and he would say the left side, but since the liar lies, he would say right. If you asked the honest twin the same question, he would say right, because he knows his brother will lie. Therefore, you would know that the correct path was the left!
Show Answer
You ask each twin What would your brother say?. This works because…. Well let’s say the correct path is on the left side. So say you asked the liar “What would your brother say?” Well, the liar would know his brother was honest and he would say the left side, but since the liar lies, he would say right. If you asked the honest twin the same question, he would say right, because he knows his brother will lie. Therefore, you would know that the correct path was the left!
The title of the problem tells you how to approach these four questions. (A). A bus leaves Moscow for Tula at noon. An hour later a cyclist leaves Tula for mosco, moving slower than the bus. When the bus and cyclist meet, which one of the two will be farther from Moscow? (B). Which is worth more: a pound of $10 gold peices or half a pound of $20 gold pieces? (C). At six o’clock the wall clock struck 6 times. Checking with my watch, I noticed the time between the first and last strokes was 30 seconds. How long will the clock take to strike 12 at midnight? (D). Three swallows fly outward from a point. When will they all be on the same plane in space? Now check the answers. Did you fall into any of the traps which lurk in these simple problems?
Answer: (A). Neither (B). A pound of metal is always more than half a pound of the same metal. (C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds. (D). There is always a plane that contains any 3 points
Solution:
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(A). Neither
(B). A pound of metal is always more than half a pound of the same metal.
(C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds.
(D). There is always a plane that contains any 3 points
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(A). Neither
(B). A pound of metal is always more than half a pound of the same metal.
(C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds.
(D). There is always a plane that contains any 3 points
(B). A pound of metal is always more than half a pound of the same metal.
(C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds.
(D). There is always a plane that contains any 3 points
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