How many honest membes are in state assmebly?
2007-08-13 08:49:48 · 14 answers · asked by Alexander 6 in Science & Mathematics ➔ Mathematics
Each member said:
"Among 100 of my colleques 75 are liars. They would tell you not necessarily the truth, but what suites them the best at the moment. As for myself, it would be unethical for me to asnwer"
2007-08-13 09:12:49 · update #1
One answer is none, in which case everyone is a liar, so anyone who says 75% of the assembly is liars, would be lying (the real % is 100%). This means that everyone is a liar, so there is no apparent contradiction. Another answer is 26.
n/101 lie.
n/100 is the % of lying colleagues for any truth-telling member.
If 75% is ever a truthful statement (<100% are liars), then
n=75
101-75 liars=26 truth tellers
Check: (n-1)/100 is the % of lying colleagues for a liar. Liars would have 74%, yet they say 75%.
P.S.: I missed the little statement, although I doubt it affects the final solution.
2007-08-13 11:47:43 · answer #1 · answered by daprofessa15 2 · 1⤊ 0⤋
none of them
If there is one factual answer, those telling the truth would give you that number while those telling a lie would give you a different number. Since they all gave the same number, they are either all telling the truth or all lying.
They cant all be telling the truth since that would mean 75 % must say something else.
they must all be lying.
You have now added additional information changing the question.
There are 26 honest members.
Example: Since everyone gave the same answer assume that eventually one of the honest ones is asked the question. If that person who we will call person "a" is honest and we are told that 25 of the other 100 will tell the truth, that is the truth.
When we substitute another honest person, person "b" we get the same answer.
Remember when we asked "a" they included "b" in the 25 honest people but not themselves. When you ask "b", the answer does not include "b" but now includes "a".
Every honest person told you there are 25 honest people not including themselves. According to the new info, the liars may or may not tell the truth. Here, interestingly, they all are lying by telling us that there are 25 honest people when in fact there are 26.
When we exclude the Liars from the 100 in question, all the honest people are in the group.
2007-08-13 09:00:30 · answer #2 · answered by who knows 2 · 0⤊ 0⤋
Well if they all say that 75% are liars, that means the 25% tell the truth. But 75% of the people telling you this information are lying to begin with. 25% of the people, however, are telling the truth so you can disregard what the other 75% told you because it isn't the truth. All 25% gave the same response saying that 75% lie, so it is safe to say there are 25.25 honest assembly members, 25 to nearest whole number.
2007-08-13 08:58:26 · answer #3 · answered by suspendedagain300 6 · 0⤊ 0⤋
26
Each of the 26 honest members has 100 colleagues, of which 75 are liars and 25 are honest. To state that 75% are liars is therefore an honest statement.
Each of the 75 lying members has 100 colleagues of which 26 are honest and 74 are liars (only 74% are liars, therefore saying 75% is a lie).
2007-08-13 08:57:29 · answer #4 · answered by Raymond 7 · 1⤊ 0⤋
This is obviously not Massachusetts, where 112 out of 101 elected members would say that all the other members were liars, and furthermore that 90% or more of them were criminally insane and should not be left unsupervised with underage barnyard animals. And, having lived there for a number of years, I'd have to say that they would be quite correct. What was the question again?
2007-08-13 08:55:35 · answer #5 · answered by John R 7 · 0⤊ 0⤋
Every member has 100 colleagues. When any honest member says '75%', it's true; so (75% of 100) = 75 of his/her 100 colleagues are liars. Therefore, there are 101-75 = 26 honest members.
(When any dishonest member answers, 26 of his colleagues are honest and (100-26) = 74 are dishonest; so when he/she answers '75%', it's a lie).
2007-08-13 08:57:27 · answer #6 · answered by Optimizer 3 · 2⤊ 0⤋
26 members are honest. In fact they have probably never told a lie in their life. Potential Jesus'. Perhaps we should start following the honest ones around and persecute then kill them. Who ever rises from the dead is the one that I will follow.
2007-08-13 08:53:38 · answer #7 · answered by Anonymous · 0⤊ 0⤋
They are really honest men at heart. It's just that there ethics have been corrupted.
2007-08-13 09:01:41 · answer #8 · answered by Anonymous · 0⤊ 0⤋
None based on statement.
2007-08-13 08:57:36 · answer #9 · answered by William R 7 · 0⤊ 0⤋
is this a trick question do u know the answer?
2007-08-13 08:59:04 · answer #10 · answered by Lizzie 2 · 0⤊ 0⤋