November 2024 - Challenge
This riddle was suggested by Hugo Pfoertner - thanks Hugo!
A tetrahedron is a polyhedron composed of four triangular faces, six straight edges, and four vertices. We can write the lengths of the edges as a list, e.g., [2,2,2,2,2,2].
The volume V of a tetrahedron with edge lengths [2,2,2,2,2,2] is an irrational number. However, setting the constant c=144, we find cV^2=128.
In the following, we keep c=144; do not pass another value of c as part of your solution.
Your goal: Find a tetrahedron with integer edge lengths different than [2,2,2,2,2,2], which also has a volume V satisfying cV^2=128. Provide your solution as the list of edge lengths.
A bonus "*" will be given for finding a tetrahedron with integer edge lengths satisfying cV^2=655.
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:
30/10/2024 @ 13:10 PM EST
Solution:
05/12/2024 @ 12:00 AM EST
List Updated:
09/12/2024 @ 15:10 PM EST
*Lazar Ilic(30/10/2024 6:59 PM IDT)
*King Pig(31/10/2024 5:45 AM IDT)
*Bertram Felgenhauer(31/10/2024 1:11 PM IDT)
*Jenna Talia(1/11/2024 3:36 AM IDT)
*Serge Batalov(1/11/2024 4:10 AM IDT)
*Arthur Vause(2/11/2024 12:14 AM IDT)
*Nolan Jiang(2/11/2024 1:32 AM IDT)
*Yi Jiang(4/11/2024 2:56 PM IDT)
*Dieter Beckerle(5/11/2024 10:44 AM IDT)
*Joaquim Carrapa(5/11/2024 1:00 PM IDT)
*Yan-Wu He(5/11/2024 4:25 PM IDT)
*Adrian Neacsu(6/11/2024 9:18 AM IDT)
*Richard Gosiorovsky(6/11/2024 8:47 PM IDT)
*Sri Mallikarjun J(8/11/2024 3:33 PM IDT)
*Marco Bellocchi(10/11/2024 7:50 PM IDT)
*Radu-Alexandru Todor(10/11/2024 9:38 PM IDT)
Michael Liepelt(10/11/2024 11:38 PM IDT)
*John Spurgeon & Kipp Johnson(11/11/2024 5:16 AM IDT)
*Sanandan Swaminathan(13/11/2024 1:31 AM IDT)
*Daniel Bitin(13/11/2024 6:12 PM IDT)
*Andreas Stiller(13/11/2024 7:27 PM IDT)
*John Tromp(13/11/2024 9:46 PM IDT)
Gary M. Gerken(15/11/2024 1:35 PM IDT)
*Alper Halbutogullari(16/11/2024 3:37 AM IDT)
*Robin Guilliou(17/11/2024 4:25 PM IDT)
Victor Chang(18/11/2024 4:35 AM IDT)
*Dan Dima(20/11/2024 8:41 AM IDT)
*Latchezar Christov(20/11/2024 3:17 PM IDT)
*David F.H. Dunkley(21/11/2024 1:48 PM IDT)
*Harald Bögeholz(21/11/2024 7:48 PM IDT)
*David Greer(24/11/2024 11:45 AM IDT)
*Michael Vahle(25/11/2024 1:52 PM IDT)
*Tim Walters(26/11/2024 3:18 AM IDT)
*Daniel Chong Jyh Tar(26/11/2024 4:20 PM IDT)
Stéphane Higueret(27/11/2024 11:55 AM IDT)
*Karl-Heinz Hofmann(28/11/2024 3:22 AM IDT)
Lorenz Reichel(29/11/2024 8:29 AM IDT)
*Kang Jin Cho(30/11/2024 7:55 AM IDT)
Chris Shannon(30/11/2024 5:16 PM IDT)
Paul Lupascu(1/12/2024 10:26 AM IDT)
*Stephen Ebert & Matthew Lee(2/12/2024 7:20 AM IDT)
*Evan Semet(2/12/2024 5:37 PM IDT)
*Blaine Hill(2/12/2024 9:28 PM IDT)
*Julian Ma(3/12/2024 11:05 AM IDT)
Li Li(4/12/2024 7:22 PM IDT)
Matt Cristina(5/12/2024 6:59 AM IDT)
*BC & E. Lam(6/12/2024 5:05 PM IDT)