1. Find the switch
There is a room with a door (closed) and three light bulbs. Outside the room there are three switches, connected to the bulbs. You may manipulate the switches as you wish, but once you open the door you can't change them. Identify each switch with its bulb.
Gee, I surprised my self by putting this age old thing here. Buy anyway.
Ans.Switch the first one on for a couple of minutes then switch it off, switch the second one on, and keep the third turned off. Get into the room, the first should be hot and not lit, the second is lit, and the third is cold and not lit.
2. 100 doors
you have 100 doors in a row that are all initially closed. you make 100 passes by the doors starting with the first door every time. the first time through you visit every door and toggle the door (if the door is closed, you open it, if its open, you close it). the second time you only visit every 2nd door (door #2, #4, #6). the third time, every 3rd door (door #3, #6, #9), etc, until you only visit the 100th door.
question: what state are the doors in after the last pass? which are open which are closed?
Ans.
solution: you can figure out that for any given door, say door #42, you will visit it for every divisor it has. so 42 has 1 & 42, 2 & 21, 3 & 14, 6 & 7. so on pass 1 i will open the door, pass 2 i will close it, pass 3 open, pass 6 close, pass 7 open, pass 14 close, pass 21 open, pass 42 close. for every pair of divisors the door will just end up back in its initial state. so you might think that every door will end up closed? well what about door #9. 9 has the divisors 1 & 9, 3 & 3. but 3 is repeated because 9 is a perfect square, so you will only visit door #9, on pass 1, 3, and 9… leaving it open at the end. only perfect square doors will be open at the end.
3. Color of Hat
Four men are lined up on some steps. They are all facing in the same direction. A wall separates the fourth man from the other three.
So to summarise: -
Man 1 can see men 2 and 3.
Man 2 can see man 3.
Man 3 can see none of the others.
Man 4 can see none of the others.
The men are wearing hats. They are told that there are two white hats and two black hats. The men initially don't know what colour hat they are wearing. They are told to shout out the colour of the hat that they are wearing as soon as they know for certain what colour it is.
They are not allowed to turn round.
They are not allowed to talk to each other.
So the question is -
Who is the first person to shout out and why
Ans.
The man who calls out is Number 2. Why?
After a short time, Number 1 has not shouted out what colour hat he is wearing. Because of this number 2 knows that he cannot be wearing the same colour hat as the person in front of him. If he was then number 1 would see two black hats and would therefore know that his hat must be white.
Armed with the knowledge that :-
He isn't wearing the same colour hat as the man in front.
The man in front is wearing a black hat.
number two can confidently shout out that the hat he is wearing is white.
4. Angle of Hour Hand
An analog clock reads 3:15. What is the angle between the minute hand and hour hand?
Ans.
12 hours on the clock make 360 deg. so one hour is 30 deg. the hour hand will be directly on the 3 when the minute hand is at 12 (3:00). after 15 minutes or 1/4 of an hour, the hour hand will be 1/4 * 30 deg = 7.5 deg. away from the minute hand.
5. Need to cross desert
An explorer wishes to cross a barren desert that requires 6 days to cross, but one man can only carry enough food for 4 days. What is the fewest number of other men required to help carry enough food for him to cross?
Ans.
Three men, each with 4-days of food head out (day 1).
The next day eachhas three days worth of food.
The first man gives one-days rations to each of the other 2. That leaves him with one day's rations to go back.
The other two, now with 4-days of rations continue (day 2)
The next day the second man gives one-days worth of rations to the third man. The second man has 2-days of rations to go back. The third man now has 4-days of rations to make the 4-day trip across the desert.
Next Puzzle here
There is a room with a door (closed) and three light bulbs. Outside the room there are three switches, connected to the bulbs. You may manipulate the switches as you wish, but once you open the door you can't change them. Identify each switch with its bulb.
Gee, I surprised my self by putting this age old thing here. Buy anyway.
Ans.Switch the first one on for a couple of minutes then switch it off, switch the second one on, and keep the third turned off. Get into the room, the first should be hot and not lit, the second is lit, and the third is cold and not lit.
2. 100 doors
you have 100 doors in a row that are all initially closed. you make 100 passes by the doors starting with the first door every time. the first time through you visit every door and toggle the door (if the door is closed, you open it, if its open, you close it). the second time you only visit every 2nd door (door #2, #4, #6). the third time, every 3rd door (door #3, #6, #9), etc, until you only visit the 100th door.
question: what state are the doors in after the last pass? which are open which are closed?
Ans.
solution: you can figure out that for any given door, say door #42, you will visit it for every divisor it has. so 42 has 1 & 42, 2 & 21, 3 & 14, 6 & 7. so on pass 1 i will open the door, pass 2 i will close it, pass 3 open, pass 6 close, pass 7 open, pass 14 close, pass 21 open, pass 42 close. for every pair of divisors the door will just end up back in its initial state. so you might think that every door will end up closed? well what about door #9. 9 has the divisors 1 & 9, 3 & 3. but 3 is repeated because 9 is a perfect square, so you will only visit door #9, on pass 1, 3, and 9… leaving it open at the end. only perfect square doors will be open at the end.
3. Color of Hat
Four men are lined up on some steps. They are all facing in the same direction. A wall separates the fourth man from the other three.
So to summarise: -
Man 1 can see men 2 and 3.
Man 2 can see man 3.
Man 3 can see none of the others.
Man 4 can see none of the others.
The men are wearing hats. They are told that there are two white hats and two black hats. The men initially don't know what colour hat they are wearing. They are told to shout out the colour of the hat that they are wearing as soon as they know for certain what colour it is.
They are not allowed to turn round.
They are not allowed to talk to each other.
So the question is -
Who is the first person to shout out and why
Ans.
The man who calls out is Number 2. Why?
After a short time, Number 1 has not shouted out what colour hat he is wearing. Because of this number 2 knows that he cannot be wearing the same colour hat as the person in front of him. If he was then number 1 would see two black hats and would therefore know that his hat must be white.
Armed with the knowledge that :-
He isn't wearing the same colour hat as the man in front.
The man in front is wearing a black hat.
number two can confidently shout out that the hat he is wearing is white.
4. Angle of Hour Hand
An analog clock reads 3:15. What is the angle between the minute hand and hour hand?
Ans.
12 hours on the clock make 360 deg. so one hour is 30 deg. the hour hand will be directly on the 3 when the minute hand is at 12 (3:00). after 15 minutes or 1/4 of an hour, the hour hand will be 1/4 * 30 deg = 7.5 deg. away from the minute hand.
5. Need to cross desert
An explorer wishes to cross a barren desert that requires 6 days to cross, but one man can only carry enough food for 4 days. What is the fewest number of other men required to help carry enough food for him to cross?
Ans.
Three men, each with 4-days of food head out (day 1).
The next day eachhas three days worth of food.
The first man gives one-days rations to each of the other 2. That leaves him with one day's rations to go back.
The other two, now with 4-days of rations continue (day 2)
The next day the second man gives one-days worth of rations to the third man. The second man has 2-days of rations to go back. The third man now has 4-days of rations to make the 4-day trip across the desert.
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