here 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?
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here 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?
Yes. Condition 2 requires that either 99 or 100 of them be liars. Condition 1 requires that 1 be honest.
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It is a trick question: the fact that there are 100 "high-powered" politicians explicitly determines that there are 100 liars. The one that is honest is clearly lying to us about it.
here 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?
Well, if I know that at least one is honest, then I must be lying to myself... ;-)
Either way, it's a trick question, and I think Pexx must have some Gnome blood in him.
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.
No no no, Pexx! Oh you poor, poor fool - you have been duped by the politicians!
No no no, Pexx! Oh you poor, poor fool - you have been duped by the politicians!Poor fools are they that allow the prevalence of dishonesty to rob them of the joy of seeing the honest among us and being able to share trust with them.
- - - Caldeathe
I must refer back to the phrase "High-powered politicians..." :-)
Mind you, no one is saying that they are bad people!
ROFL @Caldeathe Baequiannia
Adventure Time with Bonny, the only thing worth watching tonight. Especially since there is a raffle and we can get cool stuff by watching. Don't know if I want the bag or the Alpha access or both!
Aw dang it! Apparently you have to belucky enough to either know this washappening, or to have read a post about it soon enough - 'cause it appears to be over now...
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Presuming she goes at the same time next week, there is a countdown timer here to the next episode.
The warden of a circular jail is extremely hyper one day so he begins running around opening cells. The jail has 100 cells numbered from 1 to 100. He runs in a circle and opens all of the cells. Next he runs around and closes every 2nd cell (starting with cell 2, 4, 6 , etc.). If a cell is open he closes it and if a cell is closed he opens it. When he finishes running by all 100 cells he opens/closes every 3rd cell (starting with 3, 6, 9, 12 etc.), then every 4th cell (starting with 4, 8, 12, etc.) and so on. He does this until he goes around and only changes the 100th cell.
When he is done what cells will be open?
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Fult counts, Pexx notes. Ready?
1 finger
4 fingers
9 fingers
2 hands and 6 fingers
5 hands
7 hands and 1 finger
9 hands and 4 fingers
12 hands and 4 fingers
16 hands and 1 finger
20 hands
Ten cells open and lot of bandits free now. Maybe time to leave?
Those which have an odd number of whole divisors (including 1 and itself)
1
1 2
1 3
1 2 4
1 5
1 2 3 6
1 7
1 2 4 8
1 3 9
1 2 5 10
1 11
1 2 3 4 6 12
1 13
1 2 7 14
1 3 5 15
1 2 4 8 16
1 17
1 2 3 6 9 18
1 19
1 2 4 5 10 20
1 3 7 21
1 2 11 22
1 23
1 2 3 6 12 24
1 5 25
.
..
.
Open doors: 1 4 9 16 25, heh this looks familiar
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heh this looks familiar
Look! The warden is dead from exhaustment but he had time to write something with this chunk of coal.
<Fult tries to read the runes... n^2 -->(n+1)^2... which make no sense for him. Fult shakes his head in despair>Fult fears warden is dead with secret.
The cells 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 will be open. Only the cells that have two of the same factors (4 = 2 * 2) will be open because they are opened and closed the same number of times (except 1 which is just opened). Since they have the same factor twice their number of factors is odd.
"Their number of factors is odd" - and if you phrase that as the number of whole divisors including 1 and the number itself then it automatically includes 1 as an open door without it having to be considered as an exception... ;-)
Also, you need to be more specific than just "two of the same factors" since you could have, for example, 2 x 2 x 3 (two of the same factors...) or 3 x 3 x 4 - so it would have to be something like"has only factors that occur twice" or maybe "have two of each of its factors"
That makes it a little easier to see that the door is opened and closed the same number of times too.
It's a good puzzle!
Riddle: There is a story that a man and not a man
Saw and did not see a bird and not a bird
Perched on a branch and not a branch
And hit him and did not hit him with a rock and not a rock.
[How is this possible?]
Answer: A eunuch who did not see well saw a bat perched on a reed and threw a pumice stone at him which missed.
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Answer: A eunuch who did not see well saw a bat perched on a reed and threw a pumice stone at him which missed.
Hrm... I take issue with the "hit him and did not hit him" then.
Not a big deal, but good riddles should have answers that are obvious in hindsight.
Two beautiful maidens approach the village matchmaker to be matched. The matchmaker is impressed by their beauty, but even more impressed is she by the fact that they both look exactly alike.
The matchmaker asks each maiden where she lives, and their answers are the same; they live in the same house. She asks each who her father is, and their answers are the same; they have the same father. She asks for their birthdays, and they have the same birthday.
"Ah," says the matchmaker. "You are twins."
"No," say the maidens. "We're not twins."
How can this be?
Wait - does that mean that triplets are not also 3 sets of twins?