## Singapore Maths Question Solution and Very Interesting Observation (The Trickster) April 23, 2015

Posted by Richard Foote in Oracle Indexes.

OK, time to reveal the solution to the somewhat tricky Singapore maths exam question I blogged previously.

Remember, there were 10 dates:

May 13   May 15   May 19

June 13   June 14

July 16   July 18

August 14   August 15   August 16

Bowie only knew the month of my birthday, Ziggy only knew the day.

Bowie begins by saying “I don’t know when your birthday is, but I know Ziggy does not know too.”

Now the first part is obvious, Bowie only knows the month and there are at least 2 possible dates for every month, so there is no way of Bowie knowing my birthday based on just the month. However, the second part is new information, Bowie knows that Ziggy doesn’t know either. How can he claim this ?

Well, there are 2 special dates on the list, May 19 and July 18 as these are the only dates that have a unique day. If Ziggy was given one of these days (18 or 19), he would instantly know my birthday. However, Bowie who only knows the month knows that Ziggy doesn’t know my birthday. He can only claim this if the month is not May and not July because if the month he was given was one of these months, Ziggy might then know my birthday.

So my birthday must be in either June or August and we can eliminate both May and July from further consideration.

Now Ziggy can likewise perform this logic and he now knows the month of my birthday must be either June or August. He now says “At first I don’t know when your birthday is, but now I know”.

The first part is again obvious as Bowie has already stated that Ziggy doesn’t at first know my birthday. But the second part is new information, he now knows. The only way he can now know is if my birthday is one of June 13, August 15 or August 16 as these are the only dates in June and August that have a unique day. If my birthday was on either June 14 or August 14, there is no way Ziggy could now know my birthday as they both have the same day.

So we’re now down to just these 3 possible dates.

Now Bowie can also likewise perform this logic and that my birthday must be one of June 13, August 15 or August 16. The final piece of information is Bowie saying “Then I also know when your birthday is.”. The only way he can say this is if my birthday is on June 13 as this is the only remaining date with a unique month. If my birthday had been either August 15 or August 16 then there is no way for Bowie is now know.

Therefore my birthday must indeed be June 13.

So congratulations to all of you who managed to get the correct answer 🙂

An Interesting Observation

Now here’s an interesting thing. 8 people got the correct answer. But equal on top of popular answers with 8 responses also was July 16. Why was July 16 such a popular answer, when the month of July was actually one of the earliest set of dates we could eliminate from consideration. It also wasn’t one of the unique day dates which is also a common answer ? What’s so special about July 16 that so many people picked this answer ?

Well, the original Singapore question I referenced in my original blog piece in which the students had to work out Cheryl’s birthday had a correct answer of, you guessed it, July 16. You see, not only did I change the names from the original question, but I also changed the dates as well.  However, I made sure that July 16 was one of the possible 10 dates 🙂

Now I don’t know how everyone got to their answer but it strikes me as an interesting coincidence that so many people got the same answer as to the original Singapore exam question. I wonder how many people looked up the answer from the Singapore question and just assumed the same answer fit here as well ? How many people saw enough information in the question for them to assume an answer, without being careful enough regarding the actual information laid out before them ? These are two similar but yet different questions which have two different answers.

And isn’t this such a common trait, especially in the IT world when trying to diagnose a performance issue. You see a problem in which you’ve seen a similar symptom before and assume that the root cause was the same as it might have been previously, even though the information at hand (if only you looked carefully enough) is entirely different and doesn’t actually lend itself to the same root cause.

Just because the reason for lots of log file sync waits before was slow write performance to the redo log files doesn’t necessarily mean it’s the same reason today. Just because you have slow RAC cluster waits previously due to interconnect issues doesn’t necessarily mean it’s now the root cause. Quickly jumping to the wrong conclusion is such an easy mistake to make when trying to diagnose a performance problem. One needs to look carefully at all the facts on hand and with an Oracle database, there is no excuse to not look at all the relevant, appropriate facts when diagnosing a performance problem.

Hope you had some fun, I certainly did !! 🙂

1. Martin Preiss - April 23, 2015

Hi Richard,
nice. As a – more or less closely – related addition a link the story of the mathematicians and the hamster with the wooden leg from Cost Based Oracle Fundamentals – re-narrated by David Fitzjarrell: https://dfitzjarrell.wordpress.com/2011/10/27/thats-your-problem/ (maybe it’s just free assoziation).

And by the way: paranoid as I am I would not even expect to find the correct answer in the list of given dates…

Regards

Martin

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Richard Foote - April 25, 2015

Hi Martin

Yes, very nice article 🙂 And yes, it really is my birthday !!

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2. mwidlake - April 23, 2015

Something I find interesting is that a few people gave a general clue as to how they came up with the answer but not one said “I looked on the internet”.

In my experience pretty much all of us will turn to the internet for help in solving technical problems – but very few will say “I got the answer from the internet” and either passively or actively give the impression they already knew the information or solved the problem themselves.
Unless they got it from a site they think will garner their solution with more respect (eg Ask Tom).

There is nothing wrong with going to the web to help solve technical issues, otherwise all us bloggers & authors would be wasting our time. It’s how you interpret what you find 🙂

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Richard Foote - April 25, 2015

I did request that no one give away “how” they got to the answer, so that does explain why no mentioned just looking it up on the internet. Nothing wrong with searching the internet for an answer, just make sure it’s the answer to your actual question 🙂

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3. Brian Fitzgerald (@ExaGridDba) - April 23, 2015

I was prepared for a lesson on how filters work.

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4. Brian Fitzgerald (@ExaGridDba) - April 23, 2015

If a group of like-minded administrators continue to agree with each other about a diagnosis, but without effect, then look elsewhere for the solution.

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Richard Foote - April 25, 2015

Hi Brian

A movie that really had an impact on me was the original “12 Angry Men” starring a young Henry Fonda. His character disagreed with the other 11 jurors who were convinced that the man on trial was obviously guilty. Sometimes it just takes the one person to help sway a group of like minded admins and sometimes the odd one out turns out to be correct. Been there, done that 🙂

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5. WantToUnderstand - April 24, 2015

> He can only claim this if the month is not May and not July because if the month he was given was one of these months, Ziggy might then know my birthday.

How we can exclude May if it contains two dates after exluding May 19? Agree with July as there left only one day – July 16. Can you explain a bit more.

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Richard Foote - April 25, 2015

You misunderstand how Ziggy ruled out the months of May and July.

It’s not because there was just one day left after removing the unique days.

It’s because Bowie knows the correct month. If Bowie was told say May, Ziggy might have been told 19 in which case Ziggy could have known my birthday from the start. But Bowie knew with certainty that Ziggy didn’t know my birthday.

Therefore if can’t be *any* date in May. I could have stated 12 possible dates in May but if any of those days were unique and Bowie says Ziggy can’t possibly know, then it can’t be any one of those dates in May, the entire month can be ruled out with complete certainty. Bowie must therefore have been told a different month to May.

Hope you get it now 🙂

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WantToUnderstand - April 25, 2015

Sorry for my obtrusiveness. We have
May 13 May 15 May 19
June 13 June 14
July 16 July 18
August 14 August 15 August 16
We know (and Bowie also) that Ziggy does not knows your birthday therefore we can exclude unique days May 19 and July18. Now we have
May 13 May 15
June 13 June 14
July 16
August 14 August 15 August 16
As Bowie knows that Ziggy does not know your birthday and after that he claims that it does not know your birthday then Ziggy can exclude July 16 because if Bowie was told July then he would know the date. But it’s not true. Now we can exclude July 16 (And Ziggy also). But which assumptions allows us to exclude May 13 and May 15? Both dates 13 and 15 are not unique and both Bowie and Ziggy can’t exclude them. But after excluding July 16 we have
May 13 May 15
June 13 June 14
August 14 August 15 August 16
Now Ziggy knows your birthday and therefore it is August 16 because of it day uniquiness.

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6. Will Morgan - April 25, 2015

Google conspiracy theories aside I chose the incorrect date due to simple oversight. I eyeballed the list overlooking Aug 16 which would have eliminated my July 16

Quick answers shouldn’t be accompanied by vows 😛

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Richard Foote - May 4, 2015

Hi Will

Like I said, I don’t really know why/how folk picked an answer, I’m sure there are a bunch of reasons 🙂

IMHO, quick answers should only accompanied by vows if also accompanied with strong coffee !!

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7. Richard Foote - April 25, 2015

Hi WantToUnderstand

No worries, this is fun.

The flaw in your logic is this (and yes, it can be confusing !!). The part where you exclude July 16 is invalid.

You state “If Bowie was told July, he would know the date”. But if Bowie was told July, he could not have claimed at the start that Ziggy does not know. The only way for Bowie to know for certainly that Ziggy doesn’t know my birthday is to have been told a month that is not May or July.

Therefore if Bowie was told July, he could not know the date because he could not have known that Ziggy didn’t know my birthday at the very start.

Therefore your initial list of possible dates must also initially exclude all the dates from both May and July. You can’t just exclude the 2 unique dates as Bowie can’t know he can exclude these without also excluding all dates in May and July.

Hope this makes sense, although I’m not sure it does !! 🙂

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8. Scott Wesley - May 6, 2016

I arrived at July 16 because I wasn’t scribbling anywhere and my brain obviously couldn’t plan enough moves ahead. The answer slapped me in the face soon after Richard crossed out May. I eliminated 18 and 19 and thought there was a nice looking date sitting by itself.

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