There are N people in a room, each wear a birthday hat of a specific colour.
They can see other people's hats but not their own.
MAN
Scho
you can se
One of them shouted, "If you can see at least 6 yellow hats and at least 6 white hats, raise your glass!"
Exactly 12 people raised their glasses.
What is the possible value of N that fits this case?
Answers
Answer:
We know that there are 6 people with yellow hats and 6 people with white hats.
But they cannot see their hats, so there must be more people.
If there are 7+ people with a yellow hat and 7+ people with a white hat, then there are 14+ people who would raise their glasses-- more than the actual 12.
Therefore there must be 6 people with a hat of one colour (say, yellow), and more than 6 with a hat of the other colour (white).
The people with a yellow hat can see only 5 other yellow hats, so they don't raise their glasses.
But all people with a white hat will raise their glasses.
Therefore there are 12 people with white hats.
Add the 6 with a yellow hat, and we get a total of 18.
The possible value of N that fits this case is 18.
Explanation:
We know there are six people wearing yellow hats and six wearing white hats.
However, they are unable to see their hats, implying that there are more individuals present.
If there are more than 7 people wearing yellow hats and more than 7 people wearing white hats, there will be more than 14 individuals raising their glasses, which is more than the actual 12.
As a result, there must be 6 people wearing one color (say, yellow) and more than 6 wearing the other color (white).
People wearing yellow hats can only see 5 other yellow hats and so do not elevate their glasses.
However, everyone wearing a white hat will raise their glasses.
As a result, there are a total of 12 people wearing white hats.
Thus, we obtain a total of 18 when we add the 6 with the yellow cap.
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