Modern Vespa

Two brothers inherited a flock of sheep.

They sold all of them, receiving for each sheep the same number of dollars as there were sheep in the flock.

The money was paid to them in $10 bills, except the remainder (the portion owed after all possible $10 bills were given to them) was paid in $1 coins.

The two brothers placed the $10 bills in a stack on a table between them, and each brother took one of the bills followed by the other brother taking one.

The older brother took the first bill from the stack and also took the last bill.

There was still a stack of $1 coins on the table.

The younger brother took the stack of $1 coins, obviously less than $10,
and complained to his older brother, "We're not even. You owe me money.
Pay up!"

The older brother wrote him a check that squared them, i.e. both brothers ended up with the same amount from the sale of the sheep.

How much was the check for? There is only one answer.

Six dollars.

<Edited> .... scrub that ... still thinking!

Make that four dollars.

Nope. Which helps others slightly.

Two Australian brothers inherited a flock of sheep...the rest is history.

You must have responded before I posted my new answer. Is four dollars wrong?

Not four - and that helps others a lot more. I'll not respond again until someone gets it right, *and* with the reasoning.

shoot! I don't get the logic I guess. I came up with four because if we assume the older brother had $50.00 ... (just to pick a figure) and the younger brother had $40.00 plus change, and if the older brother gave the younger brother $4.00 and the change in the stack equalled $2.00, they would both end up with $46.00.

Hmm ... I'll leave it to someone else. Math never was my forte!

Five

Read the question from the beginning...

Aaaah ... I get the catch now! Thanks for the tip!

OK ... this is my last kick at the cat!

I think the answer is $2.00 ... but my head now hurts from too much logic!

The number of sheep can't be evenly divided which is why the number of $10.00 bills is not even and therefore there is some change. The only number I can come up with is that the sheep are each valued at a number ending in 6.

Six plus two = 8 and 10 minus 2 equals 8.

Two?

Correct. Well done.

Now prove it.

Geeze ... can I go eat my dinner first! This one darn near killed me!!! I hate math but love puzzles.

Three dollars.

No idea how many sheep though.

edit: oops, should read the replies more I guess

Sadly wrong. You're right that that cannot be determined.

The number of sheep in the flock is an unknown ... lets say "X".
Which means the the value of each sheep is also an unknown = "X squared".

There were an odd number of $10.00 bills in the pile meaning there had to be an odd number of sheep in the flock.

(This is where my math/logic skills become somewhat dubious ...)

By process of elimination, I came up with $2.00. Knowing that there has to be an uneven number of sheep, the math doesn't work any other way unless the amount paid is an even amount. The only even numbers left between "2" (which would be the minimum number allowable to be considered a "stack of change") and 9 (being less than 10 ... leaves 4, 6 and 8. You can't get an even answer using uneven numbers.

If the value of each sheep was $6.00 and the "stack" had at least $2.00, then 8 was the unknown quantity of dollars the younger brother had and his older brother had to give him $2.00 to even it up.

I simply did many sets of multiplications using the even numbers to find the answer I thought was right. I am probably missing a step or six in my logic ... which is why I hate math!

Well you got the answer right but the logic for getting there is slightly flawed I'm afraid - partly right though!

There needs to be an odd number of 10$ notes for the older brother to get more.

The total dollar amount is sheep*sheep

If you look at the series an odd number of 10$ notes always means the total value ends in 6

So the older bro has 4$ more than the younger, needs to give him 2 back to even it out.

Sheep $
1 1
2 4
3 9
4 16
5 25
6 36
7 49
8 64
9 81
10 100
11 121
12 144
13 169
14 196
15 225
16 256
17 289
18 324
19 361
20 400
21 441
22 484
23 529
24 576
25 625
26 676
27 729
28 784
29 841 ...

Bingo! A quirk of using number base 10.

Sorry, dinner got in the way, or I would have had the same result sooner.

Anyway, here's the next (and it isn't even Sunday yet):

We are in a forest in a strange land. There are two tribes living in that forest. One tribe will always tell the truth, one tribe will always lie. Both tribes will only answer one question to strangers.

An explorer wants to get to B and arrives at a fork. He doesn't know which way to go. A tribesman appears, but we don't know which tribe he belongs to.

So, he only has one question. How does he have to formulate the question in order to know how to get to B for sure?

It is 4:33PM in the forest, the temperature is 78F and the humidity is 99%.
The left fork leads through a ford with piranhas in the water. The right fork is infested with poisonous snakes.

The explorer is Irish, his name is Sean. I forgot his last name, but it is not relevant.

So, what's the question?

Like my Pappy used to say. "You can't beat a good sheep."

My favorites!

It rather depends on your definition of a liar - one who tells the opposite of the truth, or one whose utterances are meant to deceive.

IIRC the good answer is not to ask a question, but use a statement:
"I hear there's free beer at 'B' " and just saunter a way down one of the paths observing in which direction both the 'liar' and the truthteller go rather swiftly...

Haha, very funny!

No, that's not the correct question (!).

A liar would say yes when the truth is no, and I'll give you a hint: ask a closed question.

Actually, Jimc's response was pretty clever ... and would definately work. I'll be surprised if the real answer is better.

"If I asked the a man from the other tribe which path would he indicate
leads to B?" Take the path opposite to what's indicated!
Regardless of whom you ask, they'll point to the wrong path.

It might work, perhaps, if they even know what beer is, and you WILL be surprised when you hear the correct solution. It works 100%.

Congratulations, and you found another approach.
The solution I had in mind was this question:

"If I asked you whether this path led to B, would you say yes?"
Whatever the answer is, it is correct and can be trusted.

The first simplistic answer is "What would the other tribe say [to which way to 'B']?" and take the opposite direction.

However a good liar would get around that - cue googling for Martin Gardner and friends.

Twist the question a bit so that it stated that one fork leads to the village of the truth-tellers and one to the village of the liars and it becomes very simplistic ("Which village do you live in?" [both point to the truth-teller's village]) - but as the problem is posed no single question will elicit a 100% answer, given a good liar who will always tell the opposite of what you have 'worked out' they will say - their answer is indeterminate.

Not quite.
You don't know where which tribe lives. Actually, they live in the jungle and not in B. So you can't ask where they live.
Look at my question again. The "truth" tribesman would say yes or no, depending on the directions, and you would know where to go.
The "liar" tribesmen (assuming you are pointing to the, say, left fork, and this is indeed the correct way) would say no, if you asked him directly, but since you asked him what he would say, he has to lie about that too (to saying no), so he would say yes. This works for any fork and pointing scenario.

Ah, so you're proposing robot liars. A good human liar would have you in knots, as they mostly tell the truth!

This is one of those good questions that can't be dealt with by yes/no logic *if* we assume you are talking about human beings.

ISTR a very good mathematical answer in Scientific American circa 1972 that took deceptiveness to any one of 'n' degrees and arrived at a probability for a good hint at which fork to take. IIRC it was only about 66% probability though!

(One of the first 'fuzzy logic' thingies?)

Reading all of the information provided I came up with this:
"Tell me how to get to B or I'll shoot you in the kneecap."
Which would be effective but isn't a question.

Quite - no point in asking a possible (human) liar (of whatever degree of deceptiveness) a question. Hence my first answer...

Sorry, but this was set in stone in the problem description: Okay then, shall we move on to the next? May I again? I've got a really hard one to crack!

Oh, never mind. That one is all over the Internet when you google it.