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Brainteaser

S

Syringer

Lifer
A traveler goes to an island with a population of 100 people. Some are Liers and some are Knights. All islanders know who among them is a Lier and a Knight. Liers always lie and Knights always tell the truth.

The traveler wants to know how many are Liers and how many are Knights. He wants to do so by assembling 50 people from the island, and asking each "How many among those present here are Knights?"

The Liers organized a plan in that they agree to answer the traveler's question in such a way that independently of which 50 people he will assemble, he will always get the same set of answers.

Given that such a conspiracy is possible, find the maximal possible number of Knights that can live on the island.
 
It's late.

By same set of answers, you mean:

Person 1 will always answer 12
Person 2 will always answer 3
Person 3 will always answer 9
.
.
.
Person 50 will always answer 2

Though the numbers could be anything?
 
1?

You lost me a little with the question. So if he assembled 50 knights and the island has say 100 knights. Would they respond 50 because there's 50 people right there or 100 because there are 100 knights on the island.
 
Originally posted by: Chaotic42
It's late.

By same set of answers, you mean:

Person 1 will always answer 12
Person 2 will always answer 3
Person 3 will always answer 9
.
.
.
Person 50 will always answer 2

Though the numbers could be anything?
Click to expand...

The knights will all give the same answer, and the liers will conspire to all give the same answer..otherwise it'd be obvious who's who.

1?

You lost me a little with the question. So if he assembled 50 knights and the island has say 100 knights. Would they respond 50 because there's 50 people right there or 100 because there are 100 knights on the island.
Click to expand...

If that were the case it'd be 50.
 
Um. That doesn't make sense. All the Liars would say that they are Knights, and the Knights would point out who's a liar, but you couldn't actually tell what is what...
 
Either zero or one hundred? (so I guess the max is 100?)

The liars can't ever have the same answer as the knights (or else they would be telling the truth). So how is it possible for every one of the 50 to give the same answer unless they are all liars or all knights?

However you said there are "some" of each, so... I guess I'm stumped as to how a liar can give the same answer as a knight.
 
Your all wrong.... the answer is________________

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🙂🙂🙁🙂🙁🙂🙂🙂🙂🙂🙁🙂
🙂🙁🙂🙂🙁🙂🙂🙂🙂🙁🙂🙂
🙁🙁🙁🙁🙁🙂🙂🙂🙁🙂🙂🙂
🙂🙂🙂🙂🙁🙂🙂🙁🙁🙁🙁🙁
 
Its a trick question. The liars cannot agree to all answer the traveler's question in the same way. This is since the liars lied while agreeing. Thus they will always give answers that do not match the premise of the question.
 
Originally posted by: dullard
Its a trick question. The liars cannot agree to all answer the traveler's question in the same way. This is since the liars lied while agreeing. Thus they will always give answers that do not match the premise of the question.
Click to expand...

Oh, good one. I guess it would work if there were only one liar. But it still works for zero, and I said 100 knights first 😛
 
WOW, that whole time i was reading it as WTF is a lier?............its a shame that people can post on this board and cant spell better than a 7th grader.
 
Originally posted by: Gnrslash4life
WOW, that whole time i was reading it as WTF is a lier?............its a shame that people can post on this board and cant spell better than a 7th grader.
Click to expand...
Um, their tribe's name could be Lier. You know, the Lier tribe made up of liars.
 
This is easy and old so most of you might know it....but here's a brainteaser...

3 men walk into a restaurant, (lets call them harry, jim, steve), so harry, jim and steve have their meal and ask for the bill. the bill says £30, so harry,jim and steve decide to split the bill equally even though each of their meals cost different amounts. so each pay £10. the waiter takes the money to the till then realises he has over charged them. The real price was £25. So he decides to take £2 for himself and give back £1 each to harry jim and steve. Harry jim and steve thank the waiter for being honest and letting them know they were over charged and giving back a £3, not knowing he had taken £2 for himself.Now harry jim and steve have paid £10 each and had £1 back, meaning they have paid £9 each which = £27. So £27 plus the £2 the waiter took = £29. Where is the other £1 out of the £30?
 
Originally posted by: Buffta
This is easy and old so most of you might know it....but here's a brainteaser...
Click to expand...
Yes, it is too old, and yes we all know it. They paid £27. The restaurant made £25, and the waiter stole £2. The total recieved was £25+£2 = £27. There is no discrepancy.
 
Ignoring dullard's point and thus assuming that the Liers can negotiate a coordinated plan somehow, I think the answer is 24 Knights total = 50/2 - 1.

To be indistinguishable from the Knights, the Liers' answers must equal the number of Liers present, otherwise the traveler will realize his count does not match the answers and properly distinguish the two groups. If the split is 25/25, the Liers' strategy cannot be used because number of Liers = number of Knights, and their desired answer is coincidentally truthful.

Suggested clarification:
Add that the Liers' objective is to foil the traveler's plan.
 
Originally posted by: Buffta
This is easy and old so most of you might know it....but here's a brainteaser...

3 men walk into a restaurant, (lets call them harry, jim, steve), so harry, jim and steve have their meal and ask for the bill. the bill says £30, so harry,jim and steve decide to split the bill equally even though each of their meals cost different amounts. so each pay £10. the waiter takes the money to the till then realises he has over charged them. The real price was £25. So he decides to take £2 for himself and give back £1 each to harry jim and steve. Harry jim and steve thank the waiter for being honest and letting them know they were over charged and giving back a £3, not knowing he had taken £2 for himself.Now harry jim and steve have paid £10 each and had £1 back, meaning they have paid £9 each which = £27. So £27 plus the £2 the waiter took = £29. Where is the other £1 out of the £30?
Click to expand...

In the cash register.

As for the other question, 100.
 
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