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I'm so sorry guys, for missing Monday. sweatdrop My weekend was so busy, to be honest, I just forgot. sweatdrop So this one is worth a ******** of money, yes, I said ******** class="postcontent-align-center" style="text-align: center">THE PROBLEM

The only thing I can come up with aside from what Evelyn's said is a question for Evelyn. razz What if all three of them have white dots? I mean, sure, if we know there are two white dots and one blue then it's easy to prove, but it could go either way, couldn't it?

*had a long explanation reasoned out before she came to this blocking conclusion*

Like, he had a blue dot, and this is how it went down, baby.

Like, the youngest son sat in the room, and since no one, like, said they saw two blue dots he could deduct that a number of blue dots less than 2 existed in the room. However man, the father said he would paint either blue or white on their heads. Basically baby, He knew because nobody said he had a blue dot, yet his father said there would be a blue dot in the room.

The youngest son must have a white dot.

It would be obvious that if there were two blue dots that one of the sons would say that they saw two blue dots. Also, if one of the sons saw a blue dot on their brother and no one said that they saw two blue dots that they had a white one. But if all of the sons all saw a white dot on their brothers then they would want to believe that they got the blue dot. But no one spoke up. So I am led to believe that they all have white dots and that the father painted no blue dots to begin with to test them.

Right. From what I can see of the answers, most of them are at least partially correct, as it is a logic problem. From my perspective, here is the way the data is laid out:


Givens:
- If there are at least two blue dots, someone must say "I see two blue dots"
- No other speaking is allowed
- If a son is sure he can prove his color, they may say "I can prove my color"

Events:
- The sons are placed in formation and face each other
- Time passes
- The youngest announces he can prove his color.
- The assumption is that no other events occur.

And from such data, I will attempt to answer the question.

Cases:
(M/E == Middle/Eldest)

--------Case 1:
.................... - M/E has blue
.................... - M/E has white
The logic in this case is explained in previous posts, but I will explain it nonetheless. Assuming that all parties are truthful, logically, if the statement that there are two blue dots has not been said, it is possible to infer that one's own dot must therefore be white.

--------Case 2:
.................... - M/E has blue
.................... - M/E has blue
-------- The logic here assumes that the youngest brother does not announce that he sees two blue dots due to the fact that, first, announcing this allows both of the other brothers to prove their color, and, second, that the rule did not define that they must announce that their brothers have blue dots immediately. Assuming that the brothers know each other well, the youngest could judge by the expressions of the other brothers whether or not his dot was blue. All people will display tension on their face in some way when on the verge of a difficult decision. If neither brother's face showed the tension, the dot must be white, but if both showed tension, his dot must be blue.

--------Case 3:
.................... - M/E has white
.................... - M/E has white
-------- The logic behind this also leads to white, assuming that all brothers are roughly equal in mental capacity. From his position in seeing two white dots he can automatically infer that there are not two blue dots, and after waiting a long time, it would be certain he had a white dot, because neither of his brothers has announced their certainty before him due to the first and most logically rooted solution to the problem, seeing a white dot and a blue dot. From this, he can assume that he does not have a blue dot.

The logic behind these cases is not quite complete, but forms what must be said to be the basis of the rest of the equation. The reason the elder brothers may not have had as easy a time reading the face of the younger is also logically possible to infer. Due to watching them grow all his childhood, a younger brother would know the faces of his brothers better than they would his, which would have been less important to the developing brothers than many other things, and may have been less readable due to this lack of focus over time. This too, may not be a complete logical argument, but makes the core of any further arguments on this line.


This is what I can come up with as an answer, from my point of view. A logic problem is traditionally arranged in a table-like fashion:
This diagram displays a square table built with O used as a "content block" and colored based on values red, blue, and green. Red blocks are "blank space", formatting limits force me to use them, green blocks are squares with no set value, and blue blocks hold the variables in question. Many variants on this shape exist, often using extended versions of the table to create a formation somewhat like this:
Or some such variation on the theme, not necessarily symmetrical. The groupings of blue blocks are separated by category of information, based upon organization of data such that no two values in a section can be true of a single blue block on a perpendicular section. All in all, however, the general shape of the problem is retained regardless of the way the problem is worded, as long as it is built as a logic problem. A generic logic problem built around one of these tables would have a list of clues and a table to fill out determining the fixed values of all the blue variables in relation to each other, as the table maps a set of boolean values, and cannot be applied properly to things that have multiple truths.


All in all, I have given all ye an answer and much irrelevant data.

Peace,
Devath

Like, you could always split up the prize, Baby.

OK, so I think I figured this out. I'll just give everyone 10k.
That ends up being 60k, but whatever. D;

edit: All trades were sent except MissyRae's. She needs to buy a trading pass. >_>

I'm sorry I am still new to this... I have a trading pass now.

Thanks!