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Answer :
The only valid scenario is that all 37 creatures who answer "yes" are elves, and the number of gnomes at the Magical Cafe is 42.
To determine the number of gnomes at the Magical Cafe, we can analyze the given information and use logic to solve the problem.
We know that there are 79 creatures at the Magical Cafe, and they are all elves or gnomes.
Let's assume that the number of elves is E and the number of gnomes is G. So, E + G = 79.
We also know that each elf tells the truth if they drink tea and lies if they drink coffee, while each gnome tells the truth if they drink coffee and lies if they drink tea.
According to the information provided, 37 creatures answer "yes" when asked if they are drinking tea.
Now, let's analyze the possible scenarios:
Scenario 1: All 37 creatures who answer "yes" are elves.
In this scenario, all 37 elves are telling the truth, which means they are all drinking tea. Since each elf tells the truth if they drink tea, this scenario is valid. So, E = 37.
Substituting E = 37 into the equation E + G = 79, we can solve for G:
37 + G = 79
G = 79 - 37
G = 42
Therefore, in this scenario, there would be 42 gnomes at the Magical Cafe.
Scenario 2: Some creatures who answer "yes" are elves, and some are gnomes.
In this scenario, let's assume that x creatures who answer "yes" are elves and (37 - x) creatures who answer "yes" are gnomes.
For x elves, there are x creatures who are telling the truth and drinking tea.
For (37 - x) gnomes, there are (37 - x) creatures who are lying and drinking coffee.
Now, let's calculate the number of creatures who are lying and drinking coffee:
Number of lying creatures = Number of lying elves + Number of lying gnomes
= (37 - x) + (37 - x)
= 74 - 2x
Since each gnome tells the truth if they drink coffee, the number of lying creatures should be equal to the number of gnomes:
74 - 2x = G
We also know that the total number of creatures is 79:
E + G = 79
Substituting E = 37 - x into the equation E + G = 79, we can solve for G:
(37 - x) + G = 79
G = 79 - 37 + x
G = 42 + x
Now, we can equate the two expressions for G and solve for x:
74 - 2x = 42 + x
Moving the terms to one side:
3x = 74 - 42
3x = 32
x = 32/3
Since x represents the number of elves, and the number of creatures must be a whole number, this scenario is not valid.Hence, there are 42 gnomes at the Magical Cafe.
for such more question on valid scenario
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