The Matching Game

[NaOH]

What would be the expected number of points if one guessed randomly?

I'm probably wrong but I think it's 1 point per question, 2 points if one guesses their own responses correctly. So that's 6 points or 12. Everybody should be commended for doing much better than that!

[Simon]

Interesting math problem. The Rencontres numbers D(n, k) count permutations of n elements that leave exactly k elements fixed. There are short closed formulas for any single D(n, k), but I haven't attempted to compute the expected value, the sum of k * D(n, k) over all 0 ≤ k ≤ n with fixed n. The factorials sound like there might be a nice formula for the sum.

-- Simon

[607]

Simon's answer to question 3 caused me the widest and longest-lasting grin I've had in a while!

[Nepster]

What would be the expected number of points if one guessed randomly?
I'm probably wrong but I think it's 1 point per question, 2 points if one guesses their own responses correctly. So that's 6 points or 12. Everybody should be commended for doing much better than that!

No, you are absolutely right. The expected number of fixed points in a permutation is exactly 1. While Simon's approach works, it's probably easier to prove this via induction over the number of elements n:

For this we pick one element and consider the length of the cycle it is contained in:
Case 1) This cycle has length 1, i.e. is a fix-point. Then we still have to permute the other n-1 elements, which by induction has one more expected fix-point. So we have a total of 2 expected fix-points in this case, which occurs with probability 1/n.
Case 2) This cycle has length n. Then there is obviously no fix-point. This case occurs with probability 1/n, too.
Case 3) In all remaining cases, there are still other elements to permute, so by induction we have exactly one expected fix-point. This occurs with the remaining probability of (n-2)/n.
So in total, the expected number of fix-points is:
1/n * 2 + 1/n * 0 + (n-2)/n * 1 = 1

[Akseli]

My person specific answers (correct ones bolded):

Akseli – 1. liquorice 2. Facebook 3. glistening but pointless junk 4. athlete 5. Pokémon trainer 6. I would be clueless.
- 6/6

ccexplore – 1. vanilla 2. Google 3. gold, frankincence and myrrh 4. software engineer 5. frog trap 6. Call police, tell 2525... - 1/6

ColorfulArty – 1. strawberry 2. Nintendo Everything 3. francensence murr and gold 4. movie producer/director 5. Cranky Kong 6. Make note of what everyone else does and publish the events as a movie script. - 0/6

geoo – 1. vanilla 2. Google 3. wisdom 4. rock climber 5. Commander Keen 6. shoot the hostages - 1/6

Gronkling – 1. green tea 2. Little Fighter Empire 3. Pacifier, diapers, a soundproof box 4. musician 5. komasan 6. Tell the driver there's a bomb... - 3/6

IchoTolot – 1. chocolate 2. YouTube 3. gifts 4. medical doctor 5. Kane 6. Keep the bus just over 80,4672km/h... - 4/6

mobius – 1. mint chocolate chip 2. Aljazeera English 3. The first wise man brought him medicine... 4. CEO 5. Chell 6. Anything I want, this is America after all. - 2/6

NaOH – 1. moose tracks 2. YouTube 3. Um... Hay? 4. writer 5. sans 6. Jump of the bus and hope I survive. - 1/6

Ramon – 1. banana 2. YouTube 3. smoke 4. indie developer 5. Warren 6. It is most likely I am not on this bus... 3/6

Raymanni – 1. Anything with lots of sprinkles 2. rateyourmusic 3. lots of gold 4. composer 5. GLaDOS 6. panic - 0/6

Simon – 1. chocolate 2. Twitch 3. zip archive with backroutes 4. game developer 5. Stinky 6. If I'm the driver: Honk to make sure... 3/6


I didn't include my thought processes to avoid cluttering my guesses above, you could ask them if you're interested! Naturally I'd like to hear what people thought were my answers and why, thanks for ccexplore already giving some thought on this.

#lix logs Thursday the 15th of June 2017

[04:20:59]   <SimonN> it's scary how much I inferred from writing style
[04:21:34]   <SimonN> writing style is so much more personal than the subject written about

This was my approach also. (I am looking at you, IchoTolot question 6 with + marks and all that! )


#lix logs Friday the 16th of June 2017

[00:13:38]   <Akseli> maximum points is 66
[00:13:54]   <Akseli> I wonder what's going to be the winning score :DDD
[00:14:06]   <Akseli> I'd guess below 25

Yeah, with this many people involved, getting good points related to the maximum was really challenging.

Thanks mobius, was fun even with just 6 questions! Obviously this game tends to get exhausting especially for the Quizmaster though, yes.

[ccexplore]

Writing styles definitely helped with some of the very wordy answers like Icho's #6, but there weren't actually many of them, partly due to what some of the questions asked for.  And sometimes it misleads; for example I'm curious now how many people besides Askeli and me also guessed "mobius" for the "this is America" answer in #6?

#3 definitely have some fun answers. I'm guessing Icho's must have been floating around the net for a while, or is it original?

[IchoTolot]

Writing styles definitely helped with some of the very wordy answers like Icho's #6, but there weren't actually many of them, partly due to what some of the questions asked for.  And sometimes it misleads; for example I'm curious now how many people besides Askeli and me also guessed "mobius" for the "this is America" answer in #6?

#3 definitely have some fun answers. I'm guessing Icho's must have been floating around the net for a while, or is it original?

The answer is original

I just wanted to come up with some crazy explanations for some of the "wonders" mainly for a comedy effect.

And I really like comming up with some actual solutions for problems like the bus situation, at least so long as it's not too complicated

[Ryemanni]

This was a very fun game even though I didn't do any guessing... I still had fun reading everyone's answers!