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:
19/05/2024 @ 16:05 PM 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)