You can post the solution immediatly in a separete comment, in a hidden box, or wait for people to propose solutions, also in a hidden box. But don't let people wait for too long for the answer.
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Here is a
Hidden:
hidden box.
Last edited by ChanieMommy on Sat, Sep 26 2020, 12:16 pm; edited 4 times in total
3 men go on a business trip together.
They come to the hotel late at night.
There is a confusion, it did not say in their reservation they would arrive late.
Only one room is left , but it has three beds.
They decide to share the room.
It costs 30 Silver Dollars. They have to pay upfront.
So each of them gives 10 Silver Dollars, and they go to the room to sleep.
Next morning, when they want to leave, the receptionist sees that the night receptionist made a mistake. The room costs only 25 Silver Dollars. So he gives them back 5 Silver Dollars.
They each take one silver dollar, but, not knowing how to split the remaining two, they leave it as a tip.
Now:
Each man paid 9 silver dollars.
9x3 = 27
They gave 2 as a tip
27 + 2 = 29
Where is the 30th Silver Dollar?
Hidden:
There is no 30th.
27 = 25 +2 or
25 = 30-5
You would have to subtract the 2 dollars tip from the 27 they gave, not add them.
Here’s a good one. In the school hallway there are 100 lockers in a row. They are all closed. The first student comes in and opens every one. Then the second student comes in and closes every second one. Then the third student comes in and goes to every third locker. If it’s open, she closes it, and if it’s closed she opens it. Then the fourth does the same. And so on, until all 100 students come in. At the end of the day, how many lockers will be open, and how many will be closed, and why?
Here’s a good one. In the school hallway there are 100 lockers in a row. They are all closed. The first student comes in and opens every one. Then the second student comes in and closes every second one. Then the third student comes in and goes to every third locker. If it’s open, she closes it, and if it’s closed she opens it. Then the fourth does the same. And so on, until all 100 students come in. At the end of the day, how many lockers will be open, and how many will be closed, and why?
Here is my answer
Hidden:
The numbers that are squares of natural numbers: 1, 4, 9, 16, etc. will end up open, all the others closed.
Because a square is a x a, so it will just be opened for 1, closed for a, and opened for a^2.
Whereas numbers that are not squares go along a x b, so they will be opened for 1, closed for a, reopned for b and closed again for ab. And this scheme is also true for more complex prime factors...
The numbers that are squares of natural numbers: 1, 4, 9, 16, etc. will end up open, all the others closed.
Because a square is a x a, so it will just be opened for 1, closed for a, and opened for a^2.
Whereas numbers that are not squares go along a x b, so they will be opened for 1, closed for a, reopned for b and closed again for ab. And this scheme is also true for more complex prime factors...
Three people are standing in a row in height order with each person only seeing the person/people in front of them. There are 2 black hats and 3 white hats in a bag. They each choose a hat without looking at it and put it on. Then they are asked to guess what color the hat they are wearing is. The last tallest person, who sees what the others are wearing, says "I don't know." The middle person says, "I don't know." The first shortest person who cannot see what the others are wearing guesses his color. Which color is he wearing and how did he figure it out?
Hidden:
He's wearing a white hat.
The last man didn't know what's on his head. If the two people in front of him would be in black, he'd know he's wearing white, but he didn't know what he's wearing, so we can deduce that the two people in front of him are either both wearing white or one is in white and one is in black.
The second person didn't either know. Based on the last person's response, he knows that if the guy in front of him is wearing black, he must be wearing white. But he didn't know what's wearing, so we can deduce the person in front of him was wearing white, thus leaving him undecided of whether he's also in white or in black.
I used to love these as a teen, but wow, I got old. My eyes are just reading and my brain is simply offline. Glaze, every other locker, mental image looks interesting...wonder how one would capture that in a photo....oh! Was I supposed to calculate that?
I used to love these as a teen, but wow, I got old. My eyes are just reading and my brain is simply offline. Glaze, every other locker, mental image looks interesting...wonder how one would capture that in a photo....oh! Was I supposed to calculate that?
You are standing outside a closed door with three light switches. Inside the room there is a single lightbulb. Only one switch can be turned on when you enter the room. How do you know which switch turns the light on?
You are standing outside a closed door with three light switches. Inside the room there is a single lightbulb. Only one switch can be turned on when you enter the room. How do you know which switch turns the light on?
Three people are standing in a row in height order with each person only seeing the person/people in front of them. There are 2 black hats and 3 white hats in a bag. They each choose a hat without looking at it and put it on. Then they are asked to guess what color the hat they are wearing is. The last tallest person, who sees what the others are wearing, says "I don't know." The middle person says, "I don't know." The first shortest person who cannot see what the others are wearing guesses his color. Which color is he wearing and how did he figure it out?
Hidden:
He's wearing a white hat.
The last man didn't know what's on his head. If the two people in front of him would be in black, he'd know he's wearing white, but he didn't know what he's wearing, so we can deduce that the two people in front of him are either both wearing white or one is in white and one is in black.
The second person didn't either know. Based on the last person's response, he knows that if the guy in front of him is wearing black, he must be wearing white. But he didn't know what's wearing, so we can deduce the person in front of him was wearing white, thus leaving him undecided of whether he's also in white or in black.
