2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44
Distribute the maximum number of people among the tents, observing the conditions of settlement.
A group of 25 tired tourists wants to camp on the lake. They do not have their own tents, but there are as many as 10. The owner of the campsite is a guy with quirks. He puts forward the following conditions for settling: no more than five people can live in any two tents. What is the largest number of campers that can camp? Will the whole group fit in it?
If there is one among the tents in which four tourists have settled, then there should be one, and no more than one person should live in all other tents, so that the condition “no more than five people in any two tents” is fulfilled. Bottom line: one tent with four people, nine tents with singles. 4 + 9 = 13 people in total.
If there is one among the tents in which three tourists have settled, then there should be one, and no more than two people should live in all other tents, so that the condition “no more than five people in any two tents” is fulfilled. The bottom line is: one tent with three people, nine tents with two people. Total 3 + 9 × 2 = 21 people.
If no more than two people live in each tent, then the number of tourists in this case will be 10 × 2 = 20 people.
This means that a maximum of 21 people can live on the campground. The whole group will not be able to accommodate in it.
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The original problem can be viewed here.
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