I came up with this puzzle in Windows on Haiti (FB Edition)

[Guysanto]

I asked one Haitian to tell me the presidency he was "born under". She replied: "Mwen fèt sou xxxxx" ("I was born during the xxxx presidency"). And I said: Okay... I will ask you at the most five (5) questions to which you will answer either YES or NO, and that shall be sufficient for me to tell you precisely your actual birth date. She took my challenge and in no time at all, I was able to tell her the day, month, and year of her birth.

Now, my question to you is what Haitian President was she "born under" ?

[Guysanto]

Not knowing in advance what the questions might be is part of the mystery. In other words, telling you what the questions would be would definitely make the solution a whole lot easier. However, it would not be enough of a challenge for you.

Let me give you two clues however: MATH and Haitian History. Sorry, that's all I will say for now.

[Guysanto]

OK, I have decided to give you ONE BIG CLUE...

The "yes" and "no" answers to the 5 questions I mentioned should have suggested a binary search in an ordered list (a list of dates, that is possible birthdays). The 5 queries indicate that the cardinality of the array of dates is at most 32 (2 to the fifth power) but greater than 16 (2 to the fourth power).

That answers the math part, for the most part. Now, can you apply that to Haitian History? If you do, the contents of the questions that you asked about will quickly reveal themselves.

[Guysanto]

OK, I realize that I have engaged in quite a bit of math-speak for the uninitiated out there, but I was primarily addressing a sister that I know is quite good at math and even made it the subject of her academic studies. If I lost some of you, let me first of all attempt to explain what I said above in a more approachable way, and then I'll make the clear connection to Haitian History that obviously is still puzzling my much younger colleague.

Remember the original premise: A Haitian told me that he was born "under President XXXX", and I stated that it would take me no more than 5 yes/no questions to get to her actual birthday. That may sound astounding, but it won't be so when you examine the historical underpinnings.

As mentioned previously, my 5 yes or no questions should suggest a probing method and a very efficient one at that! In mathematics and computer programming, we refer to that algorithm as a binary search of a sorted array. The sorted array in our case represents a specific presidency in Haitian History, where the elements of the array are the dates - let's say from FIRST to LAST - of that president's time in office. Since it might take me 5 yes/no (hence, binary) questions (at most) to get to my interlocutor's actual birthdate, the number of possible dates will not be more than 32 (2 to the 5th power), but will be more than 16 (2 to the 4th power). Therefore, in order for me to sport such confidence about getting to the exact birthdate in 5 questions or less, the presidency in question must have lasted between 17 and 32 days. Now, if you know Haitian History, fairly recent at that, you would know exactly which president my interlocutor was born under, without my even revealing the contents of my questions. Of course, I will gladly tell you what they are and we may even demonstrate it by playing a little reenactment game.

I hope that you have followed my reasoning so far, even if the math is still a little mysterious (we can arrange for some math lessons in that case). The remaining mystery should easily be lifted by now. If you don't know the answer, just a little bit of research should yield it. What president have we been talking about and what were the exact dates (day/month/year) of his presidency?

If my knowledge of Haitian History is correct, then there is JUST ONE presidency that lasted a number of days (nn) between 17 and 32. Should my assumption be incorrect, then I will gleefully lick the egg off my face, because the process of discovering new historical facts is always a joyful one to me.

OK, let's get some answers now: what were the president, the start date and end date of his presidency?

Anyone?

[Guysanto]

OK... since no one else will provide the answer, I'll take it to the end and close this chapter. The one Haitian President that fits our mathematical criteria (that is a presidency lasting between 17 and 32 days) is Daniel Fignolé (May 25, 1957 – June 14, 1957).

Our interlocutor could have been born on one of these days in 1957:
May 25 - May 26 - May 27 - May 28 - May 29 - May 30 (6 days in May)
June 1/2/3/4/5/6/7/8/9/10/11/12/13/14 (14 days in June)

It is usually said that Fignolé's presidency lasted only 19 days, and that is correct. Counting both May 25 and June 14 , we have 20 possible birth dates however.

Given that historical information, it is a cinch that I can then zero in on the actual date of birth in 5 questions or less.

[Guysanto]

I wonder, have you been able to follow this or have my communication skills failed me?

[Leonel Jean-Baptiste]

Guy,
ou se ougan kounye'a?
Ban'm de twa boul bOlEt non?
Leonel

[Guysanto]

No, Leonel, you don't need to be in contact with any supernatural force to solve this mathematical problem. Pretend that you were born any day during the Fignole presidency and I'll show you that I can guess your actual birthdate using five questions or fewer.

[Shelony]

Hi all,
My first question would be: "where you born in May?"

The answer will direct me to the dates in June or May.

Shelony

[Guysanto]

All right! There is life after death, after all.

Your first question is interesting, intuitive, and also quite valid, in the sense that it does not compromise your ability to tell the birthday in 4 remaining tries. It is not the only question that you might have asked, but it is one of the valid ones. So, let's re-enact. That "Fignole baby" was born in June, actually. Therefore, the answer to your first question is: "No".

So, what would be your 2nd question, Shelony?

The ball is in your court!



[I can't believe Shelony is back. We missed you, Sister.]

[Shelony]

Hi Guy,
I miss the family too.
I have not thought about the whole serie of possible questions yet but I was hoping for the date to be in May so I would have to deal with less possible dates. But knowing that it is in June, my second question will be:
Is the date a prime number?

Shelony

[Guysanto]

Clever (almost too clever, I would say) !

The answer to your second question is : "NO". But you did well and haven't hurt your chances (incredibly enough).

You now have three questions left to ask.

[Guysanto]

From the original 20 historic dates marking Fignole's presidency
May 25 - May 26 - May 27 - May 28 - May 29 - May 30 (6 days in May)
June 1/2/3/4/5/6/7/8/9/10/11/12/13/14 (14 days in June)

we are now down to 8 possible birthdates after only 2 questions, with three rounds to go.

The remaining days are: June 1, 4, 6, 8, 9, 10, 12, 14

[Shelony]

I think I am about to "bay legen" because I have tried of some questions that could help me narrow the date down but it's more difficult than I think, especially that it can be any of the 8 dates.

I am trying one more questions and see if it helps.

Third question: Is the date smaller than 9

Shelony

[Guysanto]

Shelony, you should not "bay legen" (give up) when you are SO CLOSE to scoring.

The answer to your question is "yes". The remaining days are: June 1, 4, 6, 8.

That was your third question and now you have 2 rounds to go. THE REST SHOULD BE EASY.

[Shelony]

Ok, now I can see the light. It's easy at this point.

One possible question is: Is the date smaller than 6?

One alternate question is " Is the date a multiple of 4?

Shelony

[Guysanto]

Shelony, you are so clever! Although several of your questions were outside of the normal phrasing of the binary search algorithm that would be used by most mathematicians and computer scientists, you managed to keep in step with the systematic narrowing of the possible outcomes. To answer your fourth question (actually the first of your fourth questions), I should tell you "Yes, the birth date in question is smaller than 6." Therefore, there are only two dates left. After I answer your fifth query, I hope that everyone will have understood the basis of my little historico-mathematical problem. If not, we may continue to discuss it.

I am glad that the discussion started with Anacaona, but when she ran away from me unexpectedly, Big Sister picked up the challenge and saved her honor. I hope that she does not do the same when someone is waiting for her at the altar, because big sister will not be able to help the situation then.

[Shelony]

Guy, I did not know that my sister started the discussion but I am sure that both you and she would have followed a more mathematical sets of questions since you are both trained in numbers.

But, as I said before, I did not know where I was going when I started. I approached it one step at a time and was just hoping that I don't go beyond 5 questions.

Now my last question is: Where you born on June 4?

As for little sister doing the same when someone is waiting for her at the altar, I can say that she almost did. OK, I am just kidding. But the truth is that little sister got married on June 28th, great ceremony and celebration but she was 45 min late and on her way got an anxious call from the groom who was on time (li gen le te panse li te sove). I am happy for her but I miss her for she moved to Nevada since last week.

Shelony

[Guysanto]

WOW, I MUST HAVE A GIFT FOR RAISING THE WEDDING ISSUE, EVEN THOUGH I WAS JOKING.

Congratulations, Anacaona!!! It's funny, you told us the news when Shelony just had a baby, when Shelony was perfectly quiet about it. Now Shelony has told us the news about your wedding, when you were (and still are) completely quiet about it. And you did not invite me? Oh, I don't know how I am going to get over that!

But once again, our warmest and most sincere congratulations!

Back to Shelony: The answer to your fifth and final question is "No". And now, since you cannot ask any more questions, you have to tell me the birth date in question. Hmm....

[Shelony]

The date is June 1st 1957

Shelony

[Guysanto]

Shelony, se sa nèt. Thank you for helping me demonstrate that if we were told with certitude that a person's birthday could be guessed at in 5 questions or less [given one other piece of information, that is the name of the Haitian president the person was born under], then necessarily, that President would have to be President Damiel Fignolé. Any other president, it might have required more than 5 questions (unless you are extremely good at guessing).

Someone on the Forum told me that my thesis was not valid, because the person might have been born under President Lafontant. Ha ha! I take it as a good joke, as Lafontant held the reins of power for only 10 hours and will never be considered a constitutional president in any case. But that was a good joke!

The last thing I want to say, Shelony, is that while I don't know which year, month, or day you were born, I could deduce your exact birth date using 13 yes/no questions or fewer. Isn't math wonderful? [though, I concede, perhaps not as filled with wonders like biology which is your forte. ]

But there is no need to take on this challenge, as that one lasted LONG ENOUGH!