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Author Topic: Math Games  (Read 59759 times)

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scott_pilgrim

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Re: Math Games
« Reply #250 on: February 08, 2017, 08:08:03 pm »

(*liopoil's full submission: 14.11097115104321011131171051081059811410511710932102 10512010110032112111105110116)
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scott_pilgrim

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Re: Math Games
« Reply #251 on: February 08, 2017, 08:09:17 pm »

Round 2 submissions are due by 8pm tomorrow (Thursday).  THREAD IS STILL LOCKED.
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scott_pilgrim

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Re: Math Games
« Reply #252 on: February 08, 2017, 08:09:48 pm »

Also, I meant to mention that if you would like to /in while the thread is locked, you can do so by PM.
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scott_pilgrim

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Re: Math Games
« Reply #253 on: February 09, 2017, 08:07:57 pm »

Round 2 Results:
Calamitas   f(f((integral_0^100 f(x) dx)/100))~=3.846357253...
LaLight   76.9112=76.9112
gkrieg   49.9=49.9
Jimmmmm   (no submission)
pacovf   fixed point of f(x) closest to 37~=36.93225134...
UmbrageOfSnow   square root of 4044~=63.59245238...
schadd   23.333=23.333
sudgy   π^2*e*ϕ^2~=70.23757483...
GendoIkari   36.93225134=36.93225134
2.71828…   77=77
faust   100/3 - (110 (1 - i sqrt(3)))/(3 (-35 + 3 i sqrt(1047))^(1/3)) - 5/3 (1 + i sqrt(3)) (-35 + 3 i sqrt(1047))^(1/3)~=36.93225134...
Dylan32   4.475394282=4.475394282
Tables (no submission)
Axxle   58.435=58.435
liopoil   9.01100111...=9.01100111...
      
A=42.11836…
f(A)=61.68263...


The closest submission was UmbrageOfSnow's submission of 63.59245238... (with a difference of ~1.909818...).

There were a whole lot of opportunities for me to screw up with copy/pasting and solving stuff in this round, so I've tried to double check things, but please let me know if you catch any mistakes!  Thanks!
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scott_pilgrim

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Re: Math Games
« Reply #254 on: February 09, 2017, 08:10:42 pm »

A few players actually had more digits of precision than I displayed in the previous post.  For reference, the full submissions are here:

Dylan32: 4.475394282236265014947816902669125149925708454914878000751
GendoIkari: 36.932251341
liopoil: 9.011001110111010101100101011100110111001100100000001101100011000100100000011011100111100001110100

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scott_pilgrim

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Re: Math Games
« Reply #255 on: February 09, 2017, 08:11:36 pm »

Submissions for Round 3 are due by 8pm tomorrow night.  THREAD STILL LOCKED!
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scott_pilgrim

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Re: Math Games
« Reply #256 on: February 10, 2017, 08:00:32 pm »

THREAD UNLOCKED

Results will be posted shortly.
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Calamitas

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Re: Math Games
« Reply #257 on: February 10, 2017, 08:02:23 pm »

Kudos to faust for his R1 submission
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Dylan32

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Re: Math Games
« Reply #258 on: February 10, 2017, 08:02:49 pm »

Did you guys have any big strategy for that?
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Re: Math Games
« Reply #259 on: February 10, 2017, 08:04:26 pm »

Kudos to faust for his R1 submission

I thought about it, but not knowing the mathematical literacy of other people, it just wasn't worth it.

Did you guys have any big strategy for that?

Fixed points, or f(50). My submission for day one was a typo.
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scott_pilgrim

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Re: Math Games
« Reply #260 on: February 10, 2017, 08:04:39 pm »

Round 3 Results:

Calamitas   f((integral_0^100 f(x) dx)/100)~=64.07697656...
LaLight (no submission)
gkrieg   61.588=61.588
pacovf   f(50)~=85.35533906...
UmbrageOfSnow   sqrt(7425)~=86.1684397...
schadd   77=77
sudgy   30=30
GendoIkari   50=50
2.71828…   55=55
faust   fixed point of f(x)~=61.6684...
Dylan32   80sqrt(2)/pi~=36.01265265...
Axxle   65=65
liopoil   55.5=55.5
      
      
      
A=60.614515…
f(A)=64.06834…


Calamitas wins with an impressively close 64.07698... (only 0.008639... away).

Rules for Game 3 will be posted soon.  The thread will remain unlocked for the beginning of Game 3.
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UmbrageOfSnow

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Re: Math Games
« Reply #261 on: February 10, 2017, 08:10:10 pm »

Axxle added less chaos than I expected.

Which is pretty chaotic of him.
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pacovf

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Re: Math Games
« Reply #262 on: February 10, 2017, 08:12:15 pm »

Round 3 Results:

Calamitas   f((integral_0^100 f(x) dx)/100)~=64.07697656...
LaLight (no submission)
gkrieg   61.588=61.588
pacovf   f(50)~=85.35533906...
UmbrageOfSnow   sqrt(7425)~=86.1684397...
schadd   77=77
sudgy   30=30
GendoIkari   50=50
2.71828…   55=55
faust   fixed point of f(x)~=61.6684...
Dylan32   80sqrt(2)/pi~=36.01265265...
Axxle   65=65
liopoil   55.5=55.5
      
      
      
A=60.614515…
f(A)=64.06834…


Calamitas wins with an impressively close 64.07698... (only 0.008639... away).

Rules for Game 3 will be posted soon.  The thread will remain unlocked for the beginning of Game 3.


I think Calamitas was the right idea, assuming enough players.
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scott_pilgrim

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Re: Math Games
« Reply #263 on: February 10, 2017, 08:15:03 pm »

3. Quarters on a Chess Board

Rules
Note: The thread will remain unlocked for the first 72 hours of the game; however, this is a zero-sum game and it is not in your interest to give the other teams hints.   
Players will be split up into pairs*.  This game will only be played once.  Players will be paired up like: highest and lowest scoring players together, then second highest and second lowest, etc.   
Each pair will have one player be assigned to role A and the other assigned to role B (chosen randomly).   
Each pair will be given roughly 72 hours to communicate with each other in a QT I will send them.  After this time period, THERE IS TO BE NO COMMUNICATION AMONG PLAYERS AT ALL REGARDING THIS GAME.  The thread and QT's will be locked at that time.   
After the 72 hour communication-period is up, the player in role A will be privately given an 8x8 grid of H's and T's, representing quarters in either the heads or tails position respectively, on a chess board.   
Additionally, four squares on the board will be marked blue (good), and one will be marked red (best).   
The player in role A must choose exactly one of the quarters on the board to "flip" (change from H to T or T to H).  Submit your selection by PM to the mod within 24 hours.  (Do not copy your partner or anyone else in the PM.)   
The state of the board (excluding the red and blue squares) after the quarter has been flipped will then be sent to player B.  (Note that they will not be told which quarter was flipped.)
Player B may then choose any one square on the board, within 24 hours of receiving the board.   
Scoring is determined as follows (per player):   
Player B guesses the red square:   12
Player B guesses a blue square:   3
Player B does not guess either a blue or red square:   Negative points so that the total points among all players is 0 and the "losing" players all get the same number of points, rounding down if necessary to avoid non-integers.

If each team guesses either a blue or red square, the negative points will be distributed among the teams who guessed blue squares.  If all teams guess the red square, no one will get any points.

*Since there is an odd number of players, there will need to be one team of 3.  I'll list the teams in the next post.
« Last Edit: February 11, 2017, 10:55:43 am by scott_pilgrim »
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Calamitas

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Re: Math Games
« Reply #264 on: February 10, 2017, 08:16:55 pm »

Oh yes, I won that thing :-D
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scott_pilgrim

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Re: Math Games
« Reply #265 on: February 10, 2017, 08:19:03 pm »

Game 3 Teams:

UmbrageOfSnow (A), LaLight (B)
faust (B), GendoIkari (A)
Calamitas (B), gkrieg13 (A)
2.71828... (A), pacovf (B)
Dylan32 (B), schadd (A)
sudgy (B), Axxle (A), liopoil (can participate in planning and share in points)
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scott_pilgrim

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Re: Math Games
« Reply #266 on: February 10, 2017, 08:29:30 pm »

QT's have been sent.  Please let me know if you did not receive one, or if the link doesn't work, or the wrong player names are in the title of the QT, etc.
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scott_pilgrim

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Re: Math Games
« Reply #267 on: February 10, 2017, 08:38:56 pm »

The discussion period for Game 3 will end at 7:30pm on Monday, February 13.
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liopoil

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Re: Math Games
« Reply #268 on: February 10, 2017, 08:49:51 pm »

I was very confused by some of the guesses in that game. Why did so many people guess near 50 in round 1? Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5? Why does Calamitas' strategy make sense? Why the random square roots UoS? I just tried to guess how far off the stable equilibrium people would be guessing, and in the first two rounds I way underestimated.

Props to faust for submitting an exact fixed point all three rounds.
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UmbrageOfSnow

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Re: Math Games
« Reply #269 on: February 10, 2017, 08:55:49 pm »

I was very confused by some of the guesses in that game. Why did so many people guess near 50 in round 1? Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5? Why does Calamitas' strategy make sense? Why the random square roots UoS? I just tried to guess how far off the stable equilibrium people would be guessing, and in the first two rounds I way underestimated.

Props to faust for submitting an exact fixed point all three rounds.

I picked what I wanted my guess to be to like 1 decimal place.  Then I squared that, picked a random number close to that, and submitted the square root of that, something with a bunch of decimal places.  It was just a lazy way to have a lot of decimal places to make ties less likely.  By the 3rd one I thought there was really no chance of a tie anyway but I just did it to keep the pattern.
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Axxle

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Re: Math Games
« Reply #270 on: February 10, 2017, 08:56:06 pm »

Axxle added less chaos than I expected.

Which is pretty chaotic of him.
;)
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schadd

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Re: Math Games
« Reply #271 on: February 10, 2017, 08:59:19 pm »

Kudos to faust for his R1 submission
yeah, i thought you were gonna do that


https://www.quicktopic.com/52/H/LPSBAfmZKnBG
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Axxle

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Re: Math Games
« Reply #272 on: February 10, 2017, 09:03:08 pm »

I was very confused by some of the guesses in that game. Why did so many people guess near 50 in round 1? Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5? Why does Calamitas' strategy make sense? Why the random square roots UoS? I just tried to guess how far off the stable equilibrium people would be guessing, and in the first two rounds I way underestimated.

Props to faust for submitting an exact fixed point all three rounds.
That's pretty similar to what I was trying, although I completely failed my submission in the first round.
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scott_pilgrim

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Re: Math Games
« Reply #273 on: February 11, 2017, 12:09:53 am »


Additionally, four squares on the board will be marked blue (good), and one will be marked red (best).   
The player in role A must choose exactly one of these quarters to "flip" (change from H to T or T to H).  Submit your selection by PM to the mod within 24 hours.  (Do not copy your partner or anyone else in the PM.)   


To clarify, you may flip ANY quarter on the entire board, not just a quarter on one of the colored squares.  Sorry for the ambiguity.
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faust

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Re: Math Games
« Reply #274 on: February 11, 2017, 03:28:11 am »

Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5?
The unstable equilibrium was closer to the average value of the function.
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