May 2024 - Challenge
This problem was suggested by Lorenzo Gianferrari Pini and Radu-Alexandru Todor - thanks!
Dobble® is a card game in which each card contains eight symbols, and any two Dobble cards in the deck share exactly one symbol. A standard Dobble deck consists of 55 cards and 57 symbols. However, it is possible to have a deck of 57 cards and 57 symbols.
In general, given a number N, which is a prime power, it is possible to find a Dobble-like deck where each card contains N+1 symbols, and there are N^2+N+1 cards and symbols in the deck. Dobble itself corresponds to the case N=7.Your goal: For N=4, find the number of all possible Dobble-like decks with N^2+N+1 cards and symbols, and N+1 symbols per card, where each pair of cards has exactly one common symbol.
A Bonus "*" will be given for finding the number of all possible Dobble-like decks for N=8.
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Challenge:
30/04/2024 @ 14:30 PM EST
Solution:
05/06/2024 @ 12:00 PM EST
List Updated:
10/06/2024 @ 10:05 AM EST
*Lazar Ilic(30/4/2024 3:47 PM IDT)
*Bertram Felgenhauer(30/4/2024 8:32 PM IDT)
*Yi Jiang(30/4/2024 8:34 PM IDT)
*Daniel Copeland(1/5/2024 12:20 AM IDT)
Paul Revenant(1/5/2024 2:24 AM IDT)
Jingran Lin(1/5/2024 9:25 AM IDT)
*Yan-Wu He(1/5/2024 5:51 PM IDT)
*Alper Halbutogullari(3/5/2024 4:38 AM IDT)
*Dejan Stakic(4/5/2024 1:29 PM IDT)
*Sanandan Swaminathan(6/5/2024 12:41 PM IDT)
*Hakan Summakoğlu(6/5/2024 10:44 PM IDT)
Latchezar Christov(8/5/2024 12:15 PM IDT)
*Guglielmo Sanchini(8/5/2024 3:42 PM IDT)
Franciraldo Cavalcante(9/5/2024 4:36 AM IDT)
Alex Fleischer(9/5/2024 2:26 PM IDT)
*Guilliou Robin(9/5/2024 4:15 PM IDT)
*Vladimir Volevich(10/5/2024 7:28 PM IDT)
*King Pig(11/5/2024 2:10 AM IDT)
Daniel Chong Jyh Tar(11/5/2024 11:28 AM IDT)
Daniel Bitin(12/5/2024 1:59 AM IDT)
Martin Thorne(13/5/2024 1:03 AM IDT)
*Ward Beullens(13/5/2024 10:35 AM IDT)
Arthur Vause(13/5/2024 10:46 AM IDT)
*Ido Meisner(13/5/2024 6:05 PM IDT)
*Asaf Zimmerman(13/5/2024 11:36 PM IDT)
*Avi(14/5/2024 12:10 PM IDT)
Sri Mallikarjun J(14/5/2024 7:15 PM IDT)
Julian Ma(16/5/2024 3:46 AM IDT)
*Dieter Beckerle(16/5/2024 7:37 AM IDT)
*Victor Chang(17/5/2024 2:30 AM IDT)
*Dan Ismailescu(17/5/2024 7:35 PM IDT)
*Joaquim Carrapa(17/5/2024 9:56 PM IDT)
Andrea Andenna(18/5/2024 6:22 PM IDT)
Peter Huggins(20/5/2024 8:00 PM IDT)
*David Greer(20/5/2024 8:29 PM IDT)
Evan Semet(25/5/2024 8:38 AM IDT)
Blaine Hill(27/5/2024 10:44 AM IDT)
Gary M. Gerken(28/5/2024 1:48 AM IDT)
Nyles Heise(28/5/2024 5:32 AM IDT)
*Felipe Andrade(28/5/2024 4:30 PM IDT)
*Marco Bellocchi(29/5/2024 1:39 AM IDT)
Mark Pervovskiy(29/5/2024 10:43 PM IDT)
Jason Kim(31/5/2024 3:26 AM IDT)
*Karl Mahlburg(31/5/2024 5:39 AM IDT)
Bert Dobbelaere(31/5/2024 10:35 PM IDT)
*Motty Porat(31/5/2024 11:59 PM IDT)
Benjamin Cha(2/6/2024 7:32 PM IDT)
*Kang Jin Cho(3/6/2024 9:42 AM IDT)
Rudy Cortembert(3/6/2024 7:41 PM IDT)
Todd Will(4/6/2024 9:17 AM IDT)
*Dan Dima(4/6/2024 3:20 PM IDT)
Lorenz Reichel(4/6/2024 11:16 PM IDT)
*Matt Cristina(5/6/2024 8:18 AM IDT)