0) You get on a boat with a large boulder in it. You push the boat off into the middle of the lake where it floats. Now you take the boulder and shove it off; it sinks. Does the water level raise, sink, or stay the same? Second, now you jump off the boat, but because of your wide girth you float. What happens to the water level now?
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1) A guy walks into a coffee shop. He orders a regular coffee and sits down, and the waitress brings over the coffee. After a few minutes, he notices a cockroach at the bottom of his coffee. He immediately tells the waitress to get him a new cup instead (he probably should have walked out). After a few minutes, she walks out with a cup without a roach in it which is full and hands it to him. The guy gets up accuses the girl of giving him the same cup of coffee and demands to speak to the manager. How did he know?
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2) You are given a two strings which both at their lengths burns at variable times (differential rates, example - burn at 1 inch/sec than in an instant 4 inch/sec than back). The total amount that one string burns is one hour (i.e. both strings burn in an hour). You are given a match and are told that unless you measure 15 minutes with these strings you will be killed, what do you do?
Explanation for those who don't know what differential is. The rope/string will burn at variable rates, i.e. - the string can burn a yard a sec at one point and then burn at an inch a sec at another. All you are given is two string, both of which burn for a total of one hour. In other words, one string lit at one end will burn for a total of one hour. Same for the other string. I have given a clue here.
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(Solved by tasburrfoot7862)
3) There are 3 lights in a closed room and three switches outside. You must correlate the switches to the lights while only entering the room once. Assuming all lights are off. How do you do it?
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(Solved by tasburrfoot7862)
4) You are a detective and have found a man, hanging by his neck from a rope from the ceiling, dead. There is no furniture or place for this man to stand to get to the hanging point. The room is humid and stale at the same time. How did the man kill himself?
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(Solved by Mwilding)
5) A man lives on the top floor of his building (36th floor). Everyday he gets up cooks breakfast, prepares a lunch, kisses his wife and goes to work. One day while going to work, the elevator stops on the 16th floor, and the man suddenly cries out, "My wife is dead." After 3-5 minutes, his prediction comes true. How does he know? (not homicide, the man loved his wife)
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(Solved by dds14u)
6) 3 POWs are taken into a dark room with three chairs. The 3 chairs are lined up all facing forward (i.e. the back chair is facing the first 2 chairs, the middle chair is facing the 1st chair, the first chair is facing the wall). The men are seated and all are shown 3 white hats and 2 black hats. Each man has a random hat place on top of his head. He cannot see his own hat, but can see the color of the hats that are in front of him (the back seat can see the two front seat hats, the middle seat can see the front hat, the front seat can see nothing). Men can never take off the hats to look at them, but whoever guesses the color of their hat, can leave the POW camp. The other two will be killed. You only get one guess, and if you are wrong you are shot. AFTER AN EXTREMELY LONG TIME, one of the POWs gets up, names his hat color and walks out of the camp. Which POW according to chair placement figured it out, and what was his color?
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I have some harder ones, but that is it for now.
Solutions below.
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***Solution 0:***
The water level lowers when the boulder is dropped. It remains the same when you float.
Explanation: Imagine the boulder is flattened out to an infinitesimal sheet with the same density in it. With the same density it will still sink. It will displace the amount of water relative to its surface area. Now imagine that I take that sheet and curve it so that it barely floats. Now I have displaced the surface area of the rock plus the amount of space displace by the curvature (This is the same as saying I decreased the density of the rock so that it floats). So when something floats it displaces more water than if it sinks.
Alternate explanation: Take a piece of wood that floats. It displaces a lot of water. Now crush it in a compactor to increase the density, and it sinks. It displaces less water.
Now, since the rock's weight is held up by the boat, it will displace more water on the boat then when it sinks. Since you float either way, on the boat or by yourself (hypothetical of course), you displace the same amount of water either way.
***Solution 1:***
1) The man had sweetened his coffee. So when he tasted the coffee he knew it was the same cup. (No one got it)
***Solution 2:***
2) <Discounting the marginal human err> Light one string on both ends and light the other string on one end. When the first string burns out, use the lit end of the remaining string and light the other end. (No one got it)
Math explanation: Since the string burns at differential rates, you cannot fold the ends and do anthing of that nonsense. But since you know that the string burns at a full hour, lighting both ends will burn at half that amount (i.e. 30 minutes). If you can time thirty minutes than, if you light one end of the remaining string for 30 minutes (using the other string as a timer) you know that the string will burn for a remainder of 30 minutes. You can half that time by lighting the other end and telling the killer to start timing from then.
***Solution 3:***
3) Turn on two lights for five minutes, turn off one light switch. Check bulb for warmth but off, correlates to on turned off switch; Bulb that is on, on switch; Bulb off, off switch (Solved by tasburrfoot7862)
***Solution 4:***
4) He used a block of ice. (Solved by tasburrfoot7862)
Will post the first two if someone doesn't get it in 30 minutes.
***Solution 5:***
5) The man's wife is on life support. The elevator stopped on the 16th floor due to a power failure. Wife dies. The only way for the man to instantaniously know his wife will die is if something in the elevator told him that something has or will happen in his apartment. The most likely or simple answer is a power failure. Why would someone die after 3-5 minutes if there is a power failure.... they are on life support. (Solved by Mwilding)
***Solution 6:***
6) If 1 & 2 are black, 3 would instantaneously know white.
If 1 is black, and 3 doesn't answer immediately, 2 should realize he is white.
... Neither case fits the EXTREMELY LONG TIME.
The one condition that is equivalent in these two combonations should be switched.
The first chair POW (1) should realize that 2 and 3 cannot answer the question because his hat is white. (Solved by dds14u)
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1) A guy walks into a coffee shop. He orders a regular coffee and sits down, and the waitress brings over the coffee. After a few minutes, he notices a cockroach at the bottom of his coffee. He immediately tells the waitress to get him a new cup instead (he probably should have walked out). After a few minutes, she walks out with a cup without a roach in it which is full and hands it to him. The guy gets up accuses the girl of giving him the same cup of coffee and demands to speak to the manager. How did he know?
.................
2) You are given a two strings which both at their lengths burns at variable times (differential rates, example - burn at 1 inch/sec than in an instant 4 inch/sec than back). The total amount that one string burns is one hour (i.e. both strings burn in an hour). You are given a match and are told that unless you measure 15 minutes with these strings you will be killed, what do you do?
Explanation for those who don't know what differential is. The rope/string will burn at variable rates, i.e. - the string can burn a yard a sec at one point and then burn at an inch a sec at another. All you are given is two string, both of which burn for a total of one hour. In other words, one string lit at one end will burn for a total of one hour. Same for the other string. I have given a clue here.
.................
(Solved by tasburrfoot7862)
3) There are 3 lights in a closed room and three switches outside. You must correlate the switches to the lights while only entering the room once. Assuming all lights are off. How do you do it?
.................
(Solved by tasburrfoot7862)
4) You are a detective and have found a man, hanging by his neck from a rope from the ceiling, dead. There is no furniture or place for this man to stand to get to the hanging point. The room is humid and stale at the same time. How did the man kill himself?
..................
(Solved by Mwilding)
5) A man lives on the top floor of his building (36th floor). Everyday he gets up cooks breakfast, prepares a lunch, kisses his wife and goes to work. One day while going to work, the elevator stops on the 16th floor, and the man suddenly cries out, "My wife is dead." After 3-5 minutes, his prediction comes true. How does he know? (not homicide, the man loved his wife)
.................
(Solved by dds14u)
6) 3 POWs are taken into a dark room with three chairs. The 3 chairs are lined up all facing forward (i.e. the back chair is facing the first 2 chairs, the middle chair is facing the 1st chair, the first chair is facing the wall). The men are seated and all are shown 3 white hats and 2 black hats. Each man has a random hat place on top of his head. He cannot see his own hat, but can see the color of the hats that are in front of him (the back seat can see the two front seat hats, the middle seat can see the front hat, the front seat can see nothing). Men can never take off the hats to look at them, but whoever guesses the color of their hat, can leave the POW camp. The other two will be killed. You only get one guess, and if you are wrong you are shot. AFTER AN EXTREMELY LONG TIME, one of the POWs gets up, names his hat color and walks out of the camp. Which POW according to chair placement figured it out, and what was his color?
..................
I have some harder ones, but that is it for now.
Solutions below.
.
.
.
.
.
.
.
.
.
.
***Solution 0:***
The water level lowers when the boulder is dropped. It remains the same when you float.
Explanation: Imagine the boulder is flattened out to an infinitesimal sheet with the same density in it. With the same density it will still sink. It will displace the amount of water relative to its surface area. Now imagine that I take that sheet and curve it so that it barely floats. Now I have displaced the surface area of the rock plus the amount of space displace by the curvature (This is the same as saying I decreased the density of the rock so that it floats). So when something floats it displaces more water than if it sinks.
Alternate explanation: Take a piece of wood that floats. It displaces a lot of water. Now crush it in a compactor to increase the density, and it sinks. It displaces less water.
Now, since the rock's weight is held up by the boat, it will displace more water on the boat then when it sinks. Since you float either way, on the boat or by yourself (hypothetical of course), you displace the same amount of water either way.
***Solution 1:***
1) The man had sweetened his coffee. So when he tasted the coffee he knew it was the same cup. (No one got it)
***Solution 2:***
2) <Discounting the marginal human err> Light one string on both ends and light the other string on one end. When the first string burns out, use the lit end of the remaining string and light the other end. (No one got it)
Math explanation: Since the string burns at differential rates, you cannot fold the ends and do anthing of that nonsense. But since you know that the string burns at a full hour, lighting both ends will burn at half that amount (i.e. 30 minutes). If you can time thirty minutes than, if you light one end of the remaining string for 30 minutes (using the other string as a timer) you know that the string will burn for a remainder of 30 minutes. You can half that time by lighting the other end and telling the killer to start timing from then.
***Solution 3:***
3) Turn on two lights for five minutes, turn off one light switch. Check bulb for warmth but off, correlates to on turned off switch; Bulb that is on, on switch; Bulb off, off switch (Solved by tasburrfoot7862)
***Solution 4:***
4) He used a block of ice. (Solved by tasburrfoot7862)
Will post the first two if someone doesn't get it in 30 minutes.
***Solution 5:***
5) The man's wife is on life support. The elevator stopped on the 16th floor due to a power failure. Wife dies. The only way for the man to instantaniously know his wife will die is if something in the elevator told him that something has or will happen in his apartment. The most likely or simple answer is a power failure. Why would someone die after 3-5 minutes if there is a power failure.... they are on life support. (Solved by Mwilding)
***Solution 6:***
6) If 1 & 2 are black, 3 would instantaneously know white.
If 1 is black, and 3 doesn't answer immediately, 2 should realize he is white.
... Neither case fits the EXTREMELY LONG TIME.
The one condition that is equivalent in these two combonations should be switched.
The first chair POW (1) should realize that 2 and 3 cannot answer the question because his hat is white. (Solved by dds14u)