01 May 2026Puzzle4 minute readThis riddle was proposed by Lorenzo Gianferrari Pini and Radu-Alexandru Todor - thanks!Given a square binary matrix of order NN, A∈M(Z2)N×NA\in M(\mathbb{Z}_2)_{N\times N} such there is exactly one "1" value in each row and column of AA, we can find the lowest m>0m>0 such that Am=IA^m=I, the identity matrix.Denote by g(N)g(N) the maximum such mm when going over all the matrices in M(Z2)N×NM(\mathbb{Z}_2)_{N\times N} satisfying the above condition.For example, g(10)=30g(10)=30 and g(50)=180180g(50) = 180180.Your goal: Find g(106) mod (109+7)g(10^6)\ \text{mod}\ (10^9+7).A bonus "*" will be given for finding g(108) mod (109+7)g(10^8)\ \text{mod}\ (10^9+7).*King Pig (1/5/2026 9:49 AM IDT)*Alper Halbutogullari (1/5/2026 11:49 AM IDT)Ahmet Yuksel (1/5/2026 1:22 PM IDT)*Lazar Ilic (1/5/2026 1:51 PM IDT)*Paul Lupascu (1/5/2026 3:38 PM IDT)*Jean-François Hermant (1/5/2026 5:48 PM IDT)*Bertram Felgenhauer (1/5/2026 7:20 PM IDT)Stéphane Higueret (1/5/2026 10:37 PM IDT)Hakan Summakoğlu (2/5/2026 12:38 AM IDT)*Prashant Wankhede (2/5/2026 12:54 AM IDT)*Carter Tran (2/5/2026 3:46 AM IDT)*Jack Saleeby (2/5/2026 5:58 AM IDT)*Quentin Higueret (2/5/2026 6:03 AM IDT)*Pitiwat Chimplee (2/5/2026 2:22 PM IDT)*Richard Gosiorovsky (2/5/2026 3:09 PM IDT)David Greer (2/5/2026 5:36 PM IDT)Simon Atileh (2/5/2026 10:46 PM IDT)*Bert Dobbelaere (2/5/2026 11:10 PM IDT)*Martin Thorne (3/5/2026 5:51 AM IDT)Latchezar Christov (3/5/2026 10:15 PM IDT)Shirish Chinchalkar (3/5/2026 10:50 PM IDT)*Daniel Bitin (4/5/2026 12:30 AM IDT)*Philip Naveen (4/5/2026 5:10 AM IDT)*Franciraldo Cavalcante (4/5/2026 5:13 AM IDT)*Junyu Zhou (4/5/2026 7:30 AM IDT)*Stephen Ebert (4/5/2026 9:27 AM IDT)*Jiri Spitalsky (4/5/2026 10:38 AM IDT)Nadir S. (4/5/2026 11:46 AM IDT)*Guangxi Liu (4/5/2026 11:53 AM IDT)Michael Liepelt (4/5/2026 11:55 AM IDT)Juergen Koehl (4/5/2026 12:10 PM IDT)Hugo Pfoertner (4/5/2026 9:46 PM IDT)Dominik Reichl (4/5/2026 11:31 PM IDT)*Dawson Yao (5/5/2026 12:00 AM IDT)*Rethna Pulikkoonattu (5/5/2026 12:13 AM IDT)Jason Shaw (5/5/2026 4:22 AM IDT)*Kang Jin Cho (5/5/2026 5:15 AM IDT)Amos Guler (5/5/2026 2:35 PM IDT)*Shouky Dan & Tamir Ganor (5/5/2026 4:57 PM IDT)Jan Fricke (5/5/2026 5:01 PM IDT)*Evan Semet (5/5/2026 5:30 PM IDT)William Hakob Logian (6/5/2026 9:25 AM IDT)Mickle Jiao (6/5/2026 3:12 PM IDT)*Sanandan Swaminathan (7/5/2026 3:21 AM IDT)Siebel Goose (7/5/2026 8:06 AM IDT)*Daniel Chong Jyh Tar (7/5/2026 5:31 PM IDT)John Tromp (7/5/2026 6:57 PM IDT)Karl D’Souza (7/5/2026 10:38 PM IDT)*Arpit Shrivastava (8/5/2026 11:37 AM IDT)Trevor Nerbas (8/5/2026 7:27 PM IDT)*Liubing Yu (8/5/2026 11:26 PM IDT)Chern Arthas (9/5/2026 10:07 AM IDT)Christoph Baumgarten (9/5/2026 4:34 PM IDT)Kipp Johnson (9/5/2026 10:54 PM IDT)*Erik Hostens (12/5/2026 9:44 AM IDT)Fabio Michele Negroni (12/5/2026 7:20 PM IDT)Alex Fleischer (12/5/2026 8:24 PM IDT)Dan Dima (13/5/2026 9:32 AM IDT)Nick Trapp (14/5/2026 12:19 AM IDT)Morteza Esmaeili (15/5/2026 12:07 AM IDT)*Vladimir Volevich (15/5/2026 2:10 PM IDT)Armin Krauss (15/5/2026 5:46 PM IDT)Marc Casas (16/5/2026 1:00 AM IDT)Arthur Vause (16/5/2026 2:59 PM IDT)Dieter Beckerle (16/5/2026 6:40 PM IDT)Related postsPonder This Challenge - March 2026 - Path game on a hole-riddled chessboardPuzzleGadi Aleksandrowicz28 Feb 2026Ponder ThisPonder This Challenge - February 2026 - Blot-avoiding backgammon strategyPuzzleGadi Aleksandrowicz27 Jan 2026Ponder ThisPonder This Challenge - January 2026 - Number splitting PuzzleGadi Aleksandrowicz29 Dec 2025Ponder ThisPonder This Challenge - December 2025 - Sums of a prime and an even number PuzzleGadi Aleksandrowicz30 Nov 2025Ponder This