Posted April 11, 2014 If you randomly cut a stick (straight cuts) into four pieces, what is the probability that the resulting pieces will make a quadrilateral? Pentagon? Octagon? 0 Share this post Link to post Share on other sites

0 Posted April 13, 2014 Even in the simpler puzzle where two random cuts are to make a triangle, the probability depends on the manner that the cuts were made: (1) choose two random break points, (2) break at a random point, then break the larger piece, (3) there may be others. I take this puzzle to mean choice (1). The first cut is made a distance f from the nearer end. If neither of the next cuts falls in the portion of the stick from f to f+.5, we fail. Both probabilities are 1/2. For failure, both must happen, with a probability of 1/4. Probability of success for a quadrilateral is thus 3/4. For a pentagon, the next three cuts must fail to hit 1/2 of the stick with probability 1/8. Probability of success for a pentagon is thus 7/8. By extension, the probability of success for an n-gon is 1 - (1/2)^{n-2} 0 Share this post Link to post Share on other sites

0 Posted April 21, 2014 Even in the simpler puzzle where two random cuts are to make a triangle, the probability depends on the manner that the cuts were made: (1) choose two random break points, (2) break at a random point, then break the larger piece, (3) there may be others. I take this puzzle to mean choice (1). The first cut is made a distance f from the nearer end. If neither of the next cuts falls in the portion of the stick from f to f+.5, we fail. Both probabilities are 1/2. For failure, both must happen, with a probability of 1/4. Probability of success for a quadrilateral is thus 3/4. For a pentagon, the next three cuts must fail to hit 1/2 of the stick with probability 1/8. Probability of success for a pentagon is thus 7/8. By extension, the probability of success for an n-gon is 1 - (1/2)^{n-2} but then the answer for triangle will be = 1/2. isnt it 1/4? 0 Share this post Link to post Share on other sites

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If you randomly cut a stick (straight cuts) into four pieces, what is the probability that the resulting pieces will make a quadrilateral? Pentagon? Octagon?

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