沼泽乱局
The Marshy Mess
题目详情
You’ve ventured warily into Puzzle Forest, and as you round a bend you see a rickety bridge crossing a stream into a swampy area up ahead. Papers with line diagrams and decks of playing cards are strewn about next to the trail here. A grotesque monster climbs out from under the bridge! Upon seeing your defensive stance, it screeches, “Oh have the faeries been telling stories about me again? I’m just Hashi, the poor old bridge troll of Puzzle Forest!”
“I’m not so bad, but I do need some help arranging the spans through the four swampy fields up ahead (pictured above). Due to my trollish nature, each field has one island marked with the wrong number of bridges… sorry, I can’t help myself! I have three friends coming over to play cards later and I would love to set up the spans and correct the wrong numbers before then!”
[The answer to this puzzle is a rational number between 0 and 1, please give it accurate to 7 digits (or exactly in lowest terms).]
解析
Original Explanation
Your travels through Puzzle Forest continue with an encounter with a strange sort of bridge troll… some vague directions and a puzzle layout suggested you solve a Hashi (a.k.a. Bridges) logic puzzle with a twist: each of the four puzzles had exactly one inaccurate number.
Solving the four puzzles both revealed the correct numbers to be 5, 4, 3, and 1, and also gave a secret message: the doubled bridges spelled out the words “Prob” “no ACES” “givEn” “ShaPE”. The references to packs of playing cards connected with this message to imply we were asking for the probability a bridge hand would have no aces given the shape 5-4-3-1 of the corrected islands. This can be found going suit-by-suit, a hand with shape 5-4-3-1 would have probability
8*9*10*12/13^4=8640/28561~0.3025104…
not to have any aces.
Congrats to this month’s solvers!