Mountain Ranges A mountain range is a series of mountains connected by high ground. Consider the following fictional mountain range with 10 peaks which are ordered in a line, from 1 to 10. 1. First...


Mountain Ranges<br>A mountain range is a series of mountains connected by high ground. Consider the following<br>fictional mountain range with 10 peaks which are ordered in a line, from 1 to 10.<br>1. First Mountain - 3500 ft.<br>2. Second Mountain - 3300 ft.<br>3. Giant Mountain - 5000 ft.<br>4. Giant's Nephew - 4600 ft.<br>5. Old Giant Mountain - 4950 ft.<br>6. Old Giant's Cane Mountain - 4600 ft.<br>7. Mt. Discrete Structures - 4200 ft.<br>8. Mt. Noname - 4800 ft.<br>9. Mt. Runningoutofnames - 4725 ft. 10. Last Mountain - 4650 ft<br>We call a subset of peaks consecutive if they include all of the peaks from į toj (1si<js 10). For<br>example, First, Second, and Giant Mountain are consecutive, as are Old Giant Mountain and Old Giant's<br>Cane Mountain.<br>We will define a subrange as a maximal subset of three or more consecutive peaks in the range whose<br>elevations are all within 500 feet of each other. Maximal means that a subrange can not be a proper<br>subset of another subrange (e.g. if {1,2,3,4} were a subrange, then {1,2,3} is not a subrange because<br>{1,2,3} C {1,2,3,4}).<br>

Extracted text: Mountain Ranges A mountain range is a series of mountains connected by high ground. Consider the following fictional mountain range with 10 peaks which are ordered in a line, from 1 to 10. 1. First Mountain - 3500 ft. 2. Second Mountain - 3300 ft. 3. Giant Mountain - 5000 ft. 4. Giant's Nephew - 4600 ft. 5. Old Giant Mountain - 4950 ft. 6. Old Giant's Cane Mountain - 4600 ft. 7. Mt. Discrete Structures - 4200 ft. 8. Mt. Noname - 4800 ft. 9. Mt. Runningoutofnames - 4725 ft. 10. Last Mountain - 4650 ft We call a subset of peaks consecutive if they include all of the peaks from į toj (1si
A. You want to hike an entire subrange. Assuming you summit exactly one mountain with each<br>hike, what is the fewest number of hikes necessary to hike an entire subrange? Briefly justify the<br>answer.<br>B. Your friend wants to hike all 10 mountains. To decide the order, they will pick a new mountain<br>of a hat each week (they don't replace the mountain, once it is hiked they move on to a new one<br>until they get all 10). After how many hikes will they be guaranteed to hike an entire subrange?<br>Justify your answer. Hint: It may help to first determine the subranges.<br>Answer:<br>

Extracted text: A. You want to hike an entire subrange. Assuming you summit exactly one mountain with each hike, what is the fewest number of hikes necessary to hike an entire subrange? Briefly justify the answer. B. Your friend wants to hike all 10 mountains. To decide the order, they will pick a new mountain of a hat each week (they don't replace the mountain, once it is hiked they move on to a new one until they get all 10). After how many hikes will they be guaranteed to hike an entire subrange? Justify your answer. Hint: It may help to first determine the subranges. Answer:

Jun 04, 2022
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