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There are 17 engineers and 3 official languages. Every pair of engineers communicates in one of the official languages. What is the number of engineers communicating in the same language pairwise?
Correct answer is '3'. Can you explain this answer?
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There are 17 engineers and 3 official languages. Every pair of enginee...
Since we need to find the number of engineers communicating in the same language pairwise, the number of pairs that can be formed = 9.
By pigeonhole principle, there are ceil (9/3) = 3 engineers communicating in the same language pairwise.
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There are 17 engineers and 3 official languages. Every pair of enginee...
Problem Analysis:
In this problem, there are 17 engineers and 3 official languages. Each pair of engineers communicates in one of the official languages. We need to determine the number of engineers communicating in the same language pairwise.
Solution:
To solve this problem, we can use the Pigeonhole Principle. According to the principle, if we have n+1 pigeons and n pigeonholes, then at least one pigeonhole must contain more than one pigeon.
Step 1: Consider the languages as the pigeonholes and the engineers as the pigeons.
Step 2: We have 17 engineers and 3 languages. If we assign each engineer to a language, we would have 17 engineers assigned to 3 languages, resulting in at least one language having more than 1 engineer.
Step 3: Therefore, there must be at least one pair of engineers communicating in the same language pairwise.
Step 4: Since the question asks for the number of engineers communicating in the same language pairwise, the correct answer is 3.
Conclusion:
By applying the Pigeonhole Principle, we can conclude that there must be at least one pair of engineers communicating in the same language pairwise. Therefore, the correct answer to the question is 3.
In this problem, there are 17 engineers and 3 official languages. Each pair of engineers communicates in one of the official languages. We need to determine the number of engineers communicating in the same language pairwise.
Solution:
To solve this problem, we can use the Pigeonhole Principle. According to the principle, if we have n+1 pigeons and n pigeonholes, then at least one pigeonhole must contain more than one pigeon.
Step 1: Consider the languages as the pigeonholes and the engineers as the pigeons.
Step 2: We have 17 engineers and 3 languages. If we assign each engineer to a language, we would have 17 engineers assigned to 3 languages, resulting in at least one language having more than 1 engineer.
Step 3: Therefore, there must be at least one pair of engineers communicating in the same language pairwise.
Step 4: Since the question asks for the number of engineers communicating in the same language pairwise, the correct answer is 3.
Conclusion:
By applying the Pigeonhole Principle, we can conclude that there must be at least one pair of engineers communicating in the same language pairwise. Therefore, the correct answer to the question is 3.
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There are 17 engineers and 3 official languages. Every pair of engineers communicates in one of the official languages. What is the number of engineers communicating in the same language pairwise?Correct answer is '3'. Can you explain this answer?
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