Harder Math Riddles (3 pi each)

1. What is the value of 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1000?

2. There is a party of 100 high-powered politicians. All of them are either honest or liars. You walk in knowing two things: - At least one of them is honest. - If you take any two politicians, at least one of them is a liar. From this information, can you know how many are liars and how many are honest?

3. You are standing in front of a room with one light bulb inside of it. You cannot see if it is on or off. Outside the room there are 3 switches in the off positions. You may turn the switches any way you want to. You stop turning the switches, enter the room and know which switch controls the light bulb. How?

For 2 I think there are 99 liars and 1 honest

And is number 1 100?

hi

Those 2 are correct.

3. turn two on and one off, leave them there for like an hour, then turn one of the on ones off, when you go inside check the heat of the lightbulb. If it is hot and off, it is the last switch you turned off, if it is cold and hot, than it is the one you left off and if it is hot and on it's the one you left up.

wow, #3 seems impossible, I can't wait to see the answer!

lol, yeah #3 is an old riddle.  Remember hearing it all the way back about 30 years ago.

For the second question: 1 is honest and 99 are liars. 

Yes I said that

So we agree

Yes, that one is very easy. The only way to ensure that at least one (out of any two) is a liar, is to have only 1 honest person. Otherwise there would be a chance that you would pick two honest people.

Answers:

1. 100. Looks hard? Don't worry, just work it backwards and you'll find it very easy.

2. Yes, from the information you know 1 is honest and 99 are liars. One of them is honest satisfying the first piece of information. Then if you take the honest man and any other politician, the other politician must be a liar to satisfy the second piece of information, 'If you take any two politicians, at least one of them is a liar.' So 99 are liars.

3. You turn 2 switches "on" and leave 1 switch "off" and wait about a minute. Then enter the room, but just before you enter, turn one switch from "on" to "off". Once in the room, feel the light bulb. If it is warm, but off, it has to be the last switch you turned off. If it is on, it has to be the switch left on. If it is cold and is off, it has to be the switch you left in the off position.

@KittyOverlord 6 pi, @1e41-O 3 pi.

Yay

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3.141592653589793...

What does the lever riddle have to do with math or chess?

It requires you to think, and its a good riddle.