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Corrine played fourteen games. Who won the fourth game against whom? 4. A monk climbs a mountain. He starts at 8 a.m. and reaches the summit at noon. He spends the night on the summit, and at 8 a.m. the following morning he leaves the summit, descending the mountain following precisely the same route that he used on the day before. He reaches the bottom at noon. Prove that there is a time between 8 a.m. and noon for which the monk was at exactly the same spot on the mountain on both days. (Notice that nothing is specified about the speed at which the monk moves, neither down or up, and the monk's speed is clearly not required to be constant. Indeed the monk may rest, i.e. not move at all, for different periods on the different days, or even move backward by retracing portion(s) of his path, either up or down!)

Corrine played fourteen games. Who won the fourth game against whom? 4. A monk climbs a mountain. He starts at 8 a.m. and reaches the summit at noon. He spends the night on the summit, and at 8 a.m. the following morning he leaves the summit, descending the mountain following precisely the same route that he used on the day before. He reaches the bottom at noon. Prove that there is a time between 8 a.m. and noon for which the monk was at exactly the same spot on the mountain on both days. (Notice that nothing is specified about the speed at which the monk moves, neither down or up, and the monk's speed is clearly not required to be constant. Indeed the monk may rest, i.e. not move at all, for different periods on the different days, or even move backward by retracing portion(s) of his path, either up or down!)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Corrine played fourteen games. Who won the fourth game against whom? 4. A monk climbs a mountain. He starts at 8 a.m. and reaches the summit at noon. He spends the night on the summit, and at 8 a.m. the following morning he leaves the summit, descending the mountain following precisely the same route that he used on the day before. He reaches the bottom at noon. Prove that there is a time between 8 a.m. and noon for which the monk was at exactly the same spot on the mountain on both days. (Notice that nothing is specified about the speed at which the monk moves, neither down or up, and the monk's speed is clearly not required to be constant. Indeed the monk may rest, i.e. not move at all, for different periods on the different days, or even move backward by retracing portion(s) of his path, either up or down!)
Transcribed Image Text:Corrine played fourteen games. Who won the fourth game against whom? 4. A monk climbs a mountain. He starts at 8 a.m. and reaches the summit at noon. He spends the night on the summit, and at 8 a.m. the following morning he leaves the summit, descending the mountain following precisely the same route that he used on the day before. He reaches the bottom at noon. Prove that there is a time between 8 a.m. and noon for which the monk was at exactly the same spot on the mountain on both days. (Notice that nothing is specified about the speed at which the monk moves, neither down or up, and the monk's speed is clearly not required to be constant. Indeed the monk may rest, i.e. not move at all, for different periods on the different days, or even move backward by retracing portion(s) of his path, either up or down!)
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