Prince Puzzle: Newsletter Challenge (May 2020)

Congratulations !!! You Win....

Haha...not so smart now, are ya'...

...The blindfolds are then removed...

Please, could I have my blindfold back?

You got the nice one....her sister is the mean one....

That reminds me of Benjamin Franklin's essay on choosing an older mistress.

GA.

It's also the only way to be a fair challenge (satisfying the note) - any other case would not create equal chances.

Good, but there is a nagging assumption in here: That you are necessarily smarter or faster, giving the answer first.

Why are the others incapable or unwilling (or slower) to give the answer?

Why are the others incapable or unwilling (or slower) to give the answer?

The answer is they were in on the gag. I got fished in! #2

There are three different distributions of hats as seen by each individual.

1. Two black hats, which leaved them with the answer they are wearing a white hat.
2. A black and a white hat, if they are wearing a black hat, then one of the others would see two black hats, which is not the intension of the test, therefore they are wearing a white hat.
3. Two white hats, If they are also wearing a white hat, then that also would be acting against the intensions of the test, therefore they are wearing black.

"After some time you realize that the other prince's are unable to deduce the colour of their hat, or are unwilling to guess. What colour is your hat?"

Did not take the above into account, that situation would come about if all three where wearing white hats, giving them the option of wearing either colour, therefore the answer is they are all wearing a white hat. Acting on there hesitation I answer WHITE.

Since the other two princes are in a quandary each must be wondering that the hat on his head could be black and hence kept quiet .

The only possibility in such a situation is that all three princes were wearing white hats , and since our Hero prince knew that, declares it and wins the princess in the bargain . All this , because the others did not answer ; they were not asked !

Black. If I had a white hat then one of the others would quickly guess black because they are two white hats but the fact they are both silent is that are a blak had and a white hat so it is fifty fifty. This.. I must have a black had.

This question must be in jest. Who would ever question a womans ability, but the father, who trained the daughter well enough to doubt her judgment to choose well.

Some questions have no black-and-white answers, though...

There are 3 levels of intellectual complexity involved here. The first level is characterized by the thought that if you see 2 black hats, yours is white. The second level is characterized by the thought that if you see black and white, you must realize that because the other person with the white hat is obviously not seeing black and black (otherwise they would know first) therefore yours is white. The third level is characterized by the thought that if you see white and white, you then deduce that if the others saw white and black they would use the second level of intellectual complexity to deduce that their hat was white. Therefore since they aren’t, they are seeing white and white and therefore your hat is white. This is predicated on the assumption that the other 2 competitors are of equal intelligence, both in capacity and speed and that you are obviously superior to some extent in relation to capacity, speed or both. My observation however is that this is very likely not true, if I may understate my experience. (This is not a cut on anyone. Every person has different strengths and weaknesses in different areas, and even on different topics. I don’t consider myself to have superior intellect on any topic.) Any variance in intellectual capacity or speed throws this scenario off. One makes assumptions based on the level of intelligence of the other 2 (i.e. their ability to interpret data with the same skill and speed as the other). By definition if one wins the contest, the 3 do not have equal intelligence. Since abilities vary in the real world, anyone giving the first answer is giving it only on this inherently flawed assumption about the level of intelligence of the other 2 competitors, and therefore one could conclude that the first person giving the answer is potentially not as intelligent as the other 2, though that person is more brave, which was partly what the test was meant to discover. And if you are basing the answer “white” on the concept of perfect fairness, then if all 3 are of equal high intelligence, all 3 should have yelled out in unison “my hat is white” before they even put the hats on.

I went through the same inductive reasoning process, then realized it was like the prisoner's execution puzzle. The judge ordered the prisoner to be executed within the next seven days, then told the prisoner that he would not know when until the day when he would be executed.

In his cell, the prisoner reasoned thus: If I am still alive on Friday, I will be executed on Saturday, so I will know that day when I will be executed. Therefore Saturday is not the day I will die. That means it must be by Friday. But then if I am still alive on Thursday, I'll know it must be Friday, which would go against the judge's order, so Friday is out. Thus, using inductive reasoning to work backward from each day, he concluded that the judge's order was impossible to fulfill, so he could not be executed.

He was very surprised when they came for him on Tuesday.

This is similar to the problem of the one prince deciding whether his own hat is black or white based on the behavior of the other two princes. The only scenario that can definitely be ruled out is two black hats and one white; induction cannot be properly applied here, just as the prisoner could not correctly extend his argument beyond Saturday.

Answer is posted.