October 2025 - Challenge
This challenge focuses on mazes that are composed of an n\times m grid of rectangular cells, where each cell is connected to its four direct neighbors. For each pair of neighboring cells, either there is or is not a wall between them. The maze is constructed in such a manner that for every two cells in the maze, there is exactly one path between them - and notably, exactly one path from the beginning to the end.
Under these constraints, it can be seen there are exactly 192 mazes of size 3\times 3 (we count mazes as distinct even if they are the same up to rotation/reflection). The number of mazes grows exponentially with length; for a size of 10\times 15 as in the picture, the number of mazes is already 1.289\cdot 10^{66}, which can be stylized as "1.289e66".
Your goal: Find the number of 42\times 57 mazes. Give your result styled as above, in the form of a floating-point number with four digits of precision followed by an exact exponent.
A bonus "*" will be given for finding the number of 342\times 357 mazes. Give your result 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:
30/09/2025 @ 11:15 PM EST
Solution:
05/11/2025 @ 12:00 AM EST
List Updated:
15/10/2025 @ 14:05 PM EST
*Lazar Ilic(30/9/2025 2:26 PM IDT)
*Daniel Chong Jyh Tar(30/9/2025 2:39 PM IDT)
*Nadir S.(30/9/2025 2:48 PM IDT)
Ganor Tamir & Shouky Dan(30/9/2025 2:52 PM IDT)
*Dan Dima(30/9/2025 3:53 PM IDT)
*Paul Revenant(30/9/2025 4:01 PM IDT)
*Christoph Schmidt(30/9/2025 4:40 PM IDT)
*Prashant Wankhede(30/9/2025 5:31 PM IDT)
*Bertram Felgenhauer(30/9/2025 6:25 PM IDT)
*Paul Lupascu(30/9/2025 6:37 PM IDT)
*Hugo Pfoertner(30/9/2025 7:02 PM IDT)
*Jiri Spitalsky(30/9/2025 8:57 PM IDT)
*Alex Fleischer(30/9/2025 9:46 PM IDT)
*Stephen Ebert(30/9/2025 11:18 PM IDT)
*Sanandan Swaminathan(1/10/2025 1:53 AM IDT)
*Hakan Summakoğlu(1/10/2025 2:18 AM IDT)
*Alper Halbutogullari(1/10/2025 2:48 AM IDT)
*Guangxi Liu(1/10/2025 3:41 AM IDT)
*Gary M. Gerken(1/10/2025 6:01 AM IDT)
*Shirish Chinchalkar(1/10/2025 6:12 AM IDT)
*Martin Thorne(1/10/2025 6:51 AM IDT)
*Reda Kebbaj(1/10/2025 2:26 PM IDT)
*Juergen Koehl(1/10/2025 4:35 PM IDT)
*Fakih Karademir(1/10/2025 11:48 PM IDT)
*Abraham AJ Arshad(2/10/2025 9:09 AM IDT)
*Florian Sikora(2/10/2025 12:05 PM IDT)
*Daniel Bitin(2/10/2025 12:38 PM IDT)
*Latchezar Christov(2/10/2025 3:16 PM IDT)
*Reiner Martin(3/10/2025 12:20 AM IDT)
*Stéphane Higueret(3/10/2025 5:41 PM IDT)
*Dominik Reichl(3/10/2025 8:54 PM IDT)
*Sebastian Arellano-Rubach(4/10/2025 6:50 AM IDT)
*Peyo(4/10/2025 7:11 AM IDT)
*King Pig(4/10/2025 11:28 AM IDT)
Lorenz Reichel(4/10/2025 2:29 PM IDT)
*Justin Snopek(4/10/2025 3:08 PM IDT)
*Tim Walters(4/10/2025 7:43 PM IDT)
Alex Izvalov(4/10/2025 8:00 PM IDT)
*Khaled Alam(5/10/2025 5:59 AM IDT)
Fabio Michele Negroni(5/10/2025 10:59 AM IDT)
*Amos Guler(5/10/2025 5:19 PM IDT)
Gumpina Chaitanya(6/10/2025 7:18 AM IDT)
*Loukas Sidiropoulos(6/10/2025 12:00 PM IDT)
*Ankit Chakraborty(6/10/2025 2:30 PM IDT)
*Sergey Batalov(7/10/2025 4:31 AM IDT)
*Dieter Beckerle(7/10/2025 6:21 PM IDT)
*Jordan Payette(9/10/2025 2:10 AM IDT)
*Ignasi Guillén-Mola(9/10/2025 3:50 PM IDT)
*Marco Bellocchi(9/10/2025 4:58 PM IDT)
*Menshikov Maxim(9/10/2025 10:47 PM IDT)
*Anant Chebiam(10/10/2025 10:19 AM IDT)
*Kang Jin Cho(12/10/2025 11:23 AM IDT)