Zach Wissner-Gross @xaqwg
Math VP @Amplify. Co-Founder @SchoolYourself. Former Puzzle Editor @FiveThirtyEight. Opinions my own. he/him thefiddler.substack.com Roslyn, NY Joined July 2011-
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@GiraffeNeckMarc Well this was very ,very difficult C: Zack Taylor 1B: Zeke Bonura 2B: Zach McKinstry 3B: Zolio Versalles SS: Zach Sorensen LF: Zack Wheat CF: Zeke Wrigley RF: Zaza Harvey DH: Zeb Terry SP: Zack Greinke
#ThisWeeksFiddler @xaqwg A has x, B win %= (1-x)+x(1-x)=1-x^2. A %= x^2. A indiff point=k. Integral [(x+k)^2, {x, 0, 1-k}]=1/3 (1 - k^3) 1/3 (1-k^3) = k^2 ->k≈0.53209 A win % < k = Integral[(x+y)^2, {x, 0, k}, {y, 0, 1 - x}]= 1/12 k (4 - k^3) 1/3(1-k^3)+1/12 k(4 - k^3) ~ 45.38%
Strands #52 “This is a puzzle” 🔵🔵🔵🔵 🟡🔵 This is basically my mental thesaurus for referring to puzzles for #TheFiddler.
Congratulations to Angela Liu, Kristie Sue, Jessica Wan, and Hannah Fox for bringing home the gold! The USA Team earned first place in the 13th European Girls’ Mathematical Olympiad (EGMO), and each student also earned a gold medal for their individual performances. #TeamUSA 🥳
in #thisweeksfiddler we put two decks in a pile, then players draw cards for a while, if no card has a twin, both players win, and everyone leaves with a smile. at infinity, it's simpler to see that the chance is 1 over root e. joshmaxsilverman.github.io/2024-04-21-coo… @xaqwg
#ThisWeeksFiddler: no proofs, just vibes 🟠2 ellipses: semiaxes 2/3 and (2/3)√3, sharing a semiminor axis bisected by the circle's center 🟢3 ellipses: semiaxes 1/2 and (1/2)√3, major axes making an equilateral triangle inscribed in the circle, minor axes as circle radii
#ThisWeeksFiddler @xaqwg Two ellipse eclipse: A-2 = 4 pi/(3*sqrt(3)) Three ellipse eclipse: A-3 = pi *sqrt(3)/4 N>3 ellipse eclipse: A-N = 2 pi/(3*sqrt(3))*sin(2*pi/N) docs.google.com/spreadsheets/d…
observing a few details about how new tiles attach, the growth of two-row clusters can be analyzed one domino at a time and yields the factor described in the tweets above. wrote up the argument and calculation: github.com/joshmaxsilverm… @xaqwg
Extending #ThisWeeksFiddler by @xaqwg, I wonder what the average cluster size is in an infinite grid of random bits? Empirically, I found the answer is around 7.6023 squares.
We made a new game! The catch is that it's a math game for elementary school students. We built it for a client, but managed to also release it on Steam so that more people can play it. Introducing... ADD ASTRA! store.steampowered.com/app/2870750
#ThisWeeksFiddler @xaqwg Fun pattern this week for the extra credit: colab.research.google.com/drive/1lsMQ-2f…
#ThisWeeksFiddler by @xaqwg asks us to obtain 5 liters of water using a 10-liter container and a 3-liter container. I found 2 ways to do it, an "additive" method and a "subtractive" method.
#ThisWeeksFiddler @xaqwg The seed with toughest road in a March Madness style tourney with 2^n teams are the seeds that plays their first games vs the teams with the toughest schedules in 2^(n-1) and 2^(n-2) tourneys. Recursively, F(n)=2^n + 1 - F(n-1), F(1)=2. F ->2/3, G->5/6.
#ThisWeeksFiddler Assuming the folds on the three sides meet on an altitude of the pizza, this is the area of foil needed based on the distance from the meeting point to the vertex. The minimum is at exactly (5√3 - 5, 112.5). Extra credit: 150√3 in a wide vairety of ways??
#ThisWeeksFiddler by @xaqwg asks what is the smallest rectangular piece of foil you need to wrap up a triangular piece of pizza that is 10 inches on each side. Here is the best I came up with:
In #ThisWeeksFiddler by @xaqwg, you want to drive around a circular loop. But there’s just one gas station, and a full tank only gets you halfway around. Can your friends help you make it? Here is the full puzzle and my answer: bkgm.com/Fiddler/pdf/Sc…
#ThisWeeksFiddler by @xaqwg asks us to divide a rectangular birthday cake into 3 equal slices both in terms of frosting and in terms of cake. Here is the full puzzle and my answer: bkgm.com/Fiddler/pdf/Bi…
#ThisWeeksFiddler Extra Credit: birthday cake cutting and integrals I don't feel like solving and/or don't remember how to solve! desmos.com/calculator/brm…
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@GiraffeNeckMarc Well this was very ,very difficult C: Zack Taylor 1B: Zeke Bonura 2B: Zach McKinstry 3B: Zolio Versalles SS: Zach Sorensen LF: Zack Wheat CF: Zeke Wrigley RF: Zaza Harvey DH: Zeb Terry SP: Zack Greinke
#ThisWeeksFiddler @xaqwg A has x, B win %= (1-x)+x(1-x)=1-x^2. A %= x^2. A indiff point=k. Integral [(x+k)^2, {x, 0, 1-k}]=1/3 (1 - k^3) 1/3 (1-k^3) = k^2 ->k≈0.53209 A win % < k = Integral[(x+y)^2, {x, 0, k}, {y, 0, 1 - x}]= 1/12 k (4 - k^3) 1/3(1-k^3)+1/12 k(4 - k^3) ~ 45.38%
@MJGold It’s the only time they are STATIONARY………get it? I’ll show myself out……. 😬🙄
@xaqwg wise to gauge since e.g. 100, 1, 2 is won by player one 1, 100, 2 is won by player two
10 cards with numbers (visible) are in a pile; you & another person take turns picking from the top or bottom of the pile; at the end, the person whose 5 cards have the bigger sum wins. not looking for a solution – looking for how you might START this problem! #MTBoS #iTeachMath
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