The convention

Logic Level 2

A certain convention was exactly attended by 100 politicians. We are given the following 2 facts.

1) Jon Huntsman is present. He is known to be honest.

2) If you choose any 2 politicians randomly at the convention, at least one of them will be crooked (not honest).

Of the 100 politicians present, how many are crooked?

51 50 99 Impossible to determine from given information

7 solutions

Denton Young
Jul 7, 2015

First we have to determine how many of them are honest. By fact 1, we know at least one of them is.

If 2 or more were honest, we could pick those two randomly and invalidate fact 2. Therefore at most one of them is honest.

So exactly one of them is honest. Since 100 are present, the number who are crooked is (100 - 1) = 99.

How do we know Jon Huntsman is a republican? In the problem it never says the only people at the convention are Republicans and it never specifies that Jon Huntsman is honest.

Mike Talley - 5 years, 11 months ago

It's implied that no one was present except for the 100 Republicans. Otherwise it would have been mentioned in the problem.

I'm not sure how you get that "it never specifies that Jon Huntsman is honest" when it explicitly states that "he is known to be honest."

Denton Young - 5 years, 11 months ago

You must remember, this is a Logic problem; hence, we need to be very specific.

Rajdeep Bharati - 5 years, 7 months ago

Is 1) a fact? Grin.

Hope you liked the image that I added.

Calvin Lin Staff - 5 years, 11 months ago

1) is a fact -- he was so honest that OBAMA picked him to be ambassador to China in spite of him technically being a Republican. He was perfect for the position -- one of very few Americans, let alone American political figures, who speaks fluent Mandarin (among other qualifications.)

And that is a great image. Thank you very much for adding it!

Denton Young - 5 years, 11 months ago

The answer is WRONG!

Rajdeep Bharati - 5 years, 7 months ago

Vicky Smith
Jul 9, 2015

If there are even two honest people, then there is a chance that a 2 honest people will be chosen. Therefore, in order for it to be certain that a maximum of one honest person will be chosen, there can only be 1 or 0 honest people present. However, because Huntsman in honest and present, here will be only 1 person present that is honest. Hence there are 100-1 = 99 dishonest people

These "at least" clauses get me every time.

Alex Cagg - 5 years, 3 months ago

Naryan Shukle
May 13, 2016

The solution is simply that if we assume you pick 2 people infinite times, then the problem becomes simpler to understand. There is no specification that the same individual must be picked honest or crooked every time. Therefore, in infinite selections, every single person will be labelled as crooked, except for John, who we know is honest. So, since everyone can be picked crooked except for one, this means 99 of them have the ability to be crooked

i choose 99 fairst but i found that its too much, sorry for my write

Sumer Imran - 4 years, 10 months ago

Randy Pitts
Dec 9, 2015

This entire problem is invalid. In order to be "crooked", one must be in a position of authority. The problem merely states 100 republicans were in attendance. Therefore the technical answer would be: "Denton Young is a democrat attempting to mock the GOP through a failed attempt to be clever."

Ironically, the amount of corrupt democratic politicians by far outweighs corrupt republican officials. Refer to the book "Stealing America" authored by Dinesh D'Souza. It's very right wing biased opinion, however the facts are legitimate. The Clinton Foundation is the strongest example of democratic corruption.

Zienne Dampier
Oct 18, 2016

Is this throwing shade at politicians or

Shravani Sardeshpande
Aug 25, 2016

It is given that one of them is honest. And we have to group them all in such a way that at least one or both are crooked.so it cannot be possible to consider that half of them are honest and half are crooked because we have to group them all with each other thus if we group two honest with each other the given condition will be dissatisfied. Therefore 1 honest(already given) and 99 croooked men is the correct answer.

Daniel Smith
Jun 24, 2016

Question is easy enough. But I feel like your comment was a jab at politicians aha xD

The convention

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