June 2024 - Challenge
This riddle was suggested by Asaf Zimmerman - thanks, Asaf!
(A,B,C) is called a **Pythagorean triple** if A, B, C are positive integers and A^2+B^2=C^2.
For example, (3,4,5), (24,7,25), (20,21,29), and (1333,444,1405) are all Pythagorean triples.
We know that there's no triple such that \frac{A}{B}=\pi, because \pi is irrational, but we can try to get close to that. The triple (24,7,25) approximates \pi, but not very well, because \frac{24}{7}\approx 3.4285, so \left|\frac{24}{7}-\pi\right|<0.3, but not \left|\frac{24}{7}-\pi\right|<10^{-1}.
Your goal Find a Pythagorean triple (A,B,C) of numbers with 100 digits or less, such that \left|\frac{A}{B}-\pi\right|<10^{-20}.
Give your solution in the format
A = 24
B = 7
C = 25
A bonus "*" will be given for finding a Pythagorean triple (D,E,F) of numbers with 100 digits or less, such that \left|\frac{D}{E}-\pi\right|<10^{-95}. Give your solution in the same format as above.
We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!
We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com
Challenge:
31/05/2024 @ 09:30 AM EST
Solution:
05/07/2024 @ 10:30 AM EST
List Updated:
19/08/2024 @ 16:20 PM EST
*Lazar Ilic(31/5/2024 10:57 AM IDT)
*Jiri Spitalsky(31/5/2024 11:41 AM IDT)
*Bertram Felgenhauer(31/5/2024 2:23 PM IDT)
*Guglielmo Sanchini(31/5/2024 2:45 PM IDT)
Dan Dima(31/5/2024 4:24 PM IDT)
Giorgos Kalogeropoulos(31/5/2024 4:29 PM IDT)
Richard Gosiorovsky(31/5/2024 5:32 PM IDT)
*Hugo Pfoertner(31/5/2024 5:37 PM IDT)
*Yan-Wu He(31/5/2024 5:53 PM IDT)
*Yi Jiang(31/5/2024 9:17 PM IDT)
*Harald Bögeholz(31/5/2024 10:07 PM IDT)
*David Greer(31/5/2024 10:13 PM IDT)
Arthur Vause(31/5/2024 10:14 PM IDT)
*Bert Dobbelaere(1/6/2024 12:05 AM IDT)
*Serge Batalov(1/6/2024 12:25 AM IDT)
*Sanandan Swaminathan(1/6/2024 5:16 AM IDT)
*Karl Mahlburg(1/6/2024 6:06 AM IDT)
*Marco Bellocchi(1/6/2024 4:05 PM IDT)
*Daniel Chong Jyh Tar(1/6/2024 7:06 PM IDT)
*King Pig(1/6/2024 8:25 PM IDT)
*Mark Beyleveld(1/6/2024 11:51 PM IDT)
*Blaine Hill(2/6/2024 1:57 AM IDT)
*Kurt Foster(2/6/2024 3:18 AM IDT)
Rashid Naimi(2/6/2024 6:21 AM IDT)
Gary M. Gerken(2/6/2024 8:15 AM IDT)
*Oscar Volpatti(2/6/2024 9:35 AM IDT)
*Albert Stadler(2/6/2024 9:46 AM IDT)
Emmanuel Lazard(2/6/2024 3:42 PM IDT)
*Mathias Schenker(2/6/2024 4:39 PM IDT)
*Andrew Gauld(2/6/2024 5:19 PM IDT)
Julian Ma(2/6/2024 6:31 PM IDT)
Dieter Beckerle(2/6/2024 7:16 PM IDT)
*Juergen Koehl(2/6/2024 9:11 PM IDT)
*Guangxi Liu(3/6/2024 7:53 AM IDT)
*Alper Halbutogullari(3/6/2024 8:11 AM IDT)
*Vladimir Volevich(3/6/2024 1:13 PM IDT)
*Dan Dima(3/6/2024 2:36 PM IDT)
*Lorenz Reichel(3/6/2024 3:36 PM IDT)
*Dan Ismailescu(3/6/2024 11:07 PM IDT)
*Justin Snopek(3/6/2024 11:59 PM IDT)
Phil Proudman(4/6/2024 2:35 AM IDT)
*Cameron Ritson(4/6/2024 5:30 AM IDT)
José Eduardo Gaboardi de Carvalho(4/6/2024 5:31 AM IDT)
*Tim Walters(4/6/2024 9:09 AM IDT)
*Paul Lupascu(4/6/2024 3:06 PM IDT)
*Joaquim Carrapa(4/6/2024 5:44 PM IDT)
*Amos Guler(4/6/2024 6:50 PM IDT)
*John Tromp(4/6/2024 8:08 PM IDT)
*Latchezar Christov(4/6/2024 9:06 PM IDT)
Christoph Baumgarten(4/6/2024 11:31 PM IDT)
*Lu Wang(5/6/2024 12:12 AM IDT)
*Jan Fricke(5/6/2024 12:41 AM IDT)
*Arthur Vause(5/6/2024 10:23 AM IDT)
Nivrutti Tambe(5/6/2024 4:26 PM IDT)
Loukas Sidiropoulos(5/6/2024 5:36 PM IDT)
*Reiner Martin(5/6/2024 10:31 PM IDT)
Michael Liepelt(5/6/2024 11:04 PM IDT)
*Kipp Johnson(5/6/2024 11:34 PM IDT)
*Zheng Yu(6/6/2024 4:37 AM IDT)
*Xiao Liu(6/6/2024 6:31 AM IDT)
*Daniel Bitin(6/6/2024 10:47 AM IDT)
*Sachal Mahajan(7/6/2024 12:54 AM IDT)
*Evan Semet(7/6/2024 1:36 AM IDT)
*Wolfgang Kais(7/6/2024 2:31 PM IDT)
*Hakan Summakoğlu(7/6/2024 5:44 PM IDT)
*Ido Meisner(7/6/2024 6:04 PM IDT)
*Keith Kaplan(8/6/2024 4:27 AM IDT)
Paul Revenant(8/6/2024 11:24 AM IDT)
*Andrea Andenna(8/6/2024 5:28 PM IDT)
*Alex Izvalov(8/6/2024 10:22 PM IDT)
*Mark Pervovskiy(9/6/2024 2:24 AM IDT)
*David F.H. Dunkley(9/6/2024 2:33 AM IDT)
Shirish Chinchalkar(9/6/2024 3:41 AM IDT)
*Eden Saig(9/6/2024 10:24 AM IDT)
Fabio Michele Negroni(9/6/2024 3:23 PM IDT)
Thomas Egense(10/6/2024 4:13 PM IDT)
Karl-Heinz Hofmann(10/6/2024 8:26 PM IDT)
*Martin Thorne(10/6/2024 9:48 PM IDT)
*Matt Cristina(10/6/2024 9:48 PM IDT)
Guillaume Dujardin(11/6/2024 1:35 AM IDT)
*Hansraj Nahata(11/6/2024 4:09 AM IDT)
Piyush Agrawal(11/6/2024 2:22 PM IDT)
*Victor Chang(11/6/2024 3:06 PM IDT)
*Daniel Copeland(11/6/2024 11:34 PM IDT)
*Benjamin Cha(13/6/2024 1:07 AM IDT)
*Andreas Stiller(13/6/2024 2:27 AM IDT)
*Kay Lee(13/6/2024 3:06 AM IDT)
*Lawrence Au(13/6/2024 8:02 PM IDT)
*Dezhi Zhao(13/6/2024 11:55 PM IDT)
*Kevin Bauer(14/6/2024 1:48 AM IDT)
*Dieter Beckerle(14/6/2024 7:49 AM IDT)
Aviv Nisgav(15/6/2024 11:35 PM IDT)
Stefan Wirth(16/6/2024 5:06 PM IDT)
Adrian Neacsu(17/6/2024 1:21 AM IDT)
Andreas Knüpfer(17/6/2024 5:08 PM IDT)
*Erik Hostens(18/6/2024 5:32 PM IDT)
*Dillon Davis(18/6/2024 6:45 PM IDT)
*Li Li(20/6/2024 1:47 AM IDT)
*Ganghun Kim(20/6/2024 4:40 PM IDT)
*Kang Jin Cho(20/6/2024 8:22 PM IDT)
*Govind Jujare(20/6/2024 8:56 PM IDT)
*Zoltan Haindrich(21/6/2024 5:15 PM IDT)
Wenjie Yang(21/6/2024 11:39 PM IDT)
*Logan Dooley(22/6/2024 6:49 PM IDT)
Rudy Cortembert(23/6/2024 4:50 PM IDT)
Todd Will(23/6/2024 9:58 PM IDT)
Björn Hendriks(24/6/2024 3:42 AM IDT)
*Pål Hermunn Johansen(24/6/2024 4:47 PM IDT)
*Eran Vered(24/6/2024 6:49 PM IDT)
Nyles Heise(26/6/2024 4:29 AM IDT)
Stéphane Higueret(26/6/2024 8:01 AM IDT)
*Alain Michiels(26/6/2024 12:47 PM IDT)
Robin Guilliou(26/6/2024 1:51 PM IDT)
Deepak Bal(27/6/2024 10:33 PM IDT)
*Yunkyu (Luke) Lee(28/6/2024 5:57 PM IDT)
*Sofia Kozlova(29/6/2024 1:53 AM IDT)
*Suyeong Hahn(29/6/2024 5:02 PM IDT)
*Lorcan O'Connor(30/6/2024 12:19 AM IDT)
*Franciraldo Cavalcante(30/6/2024 6:53 AM IDT)
Erik Wünstel(30/6/2024 8:27 PM IDT)
*Motty Porat(30/6/2024 11:28 PM IDT)
Jeffrey Curtis(1/7/2024 7:24 AM IDT)
Thomas Watson & Steffan Môn & Joshua Burland & Vishva Patel(2/7/2024 4:24 PM IDT)
Radu-Alexandru Todor(4/7/2024 2:27 AM IDT)
*Nicholas Daskalovic(4/7/2024 6:05 AM IDT)
*Jared Kittleson(4/7/2024 4:35 PM IDT)