For your son’s sixth birthday, you’ve promised to get him the cutest creature in creation: the cuddly. It’s hard to believe that it’s a cousin of the terrifying duddly or the hideous fuddly. They’re all members of the Wuddly species, and the process of adopting them is deeply peculiar.
你兒子六歲生日到了, 你答應過他, 要給他最可愛的生物:酷迪。 難以置信的是, 牠的表親是駭人的杜迪 或醜陋的法迪。 牠們都是瓦迪種族的成員, 而領養牠們的過程也非常特殊。
It takes 100 eggs to make a single animal in genus Wuddly. When 100 eggs are placed together in an incubator, they undergo egg fusion, and combine in the following way. Blue and purple combine to make red eggs. Red and blue combine to make purple eggs, and red and purple combine to make blue eggs.
要一百顆蛋才能產生 一隻瓦迪種的動物。 把一百顆蛋放在孵蛋器當中, 它們會依照下列規則進行蛋融合: 藍色和紫色會結合成紅色的蛋。 紅色和藍色會結合成紫色的蛋。 紅色和紫色會結合成藍色的蛋。
The most plentiful eggs pair up first, and if two piles are even, an egg comes from one of them at random. They keep combining until there’s just one left. If the final egg is blue, a Cuddly hatches out of it. Purple eggs give you Duddlies, and Red eggs give you Fuddlies.
蛋最多的那一堆優先配對, 如果有兩堆蛋數量一樣, 會隨機從其中一堆取一顆。 它們會不斷結合, 直到最後剩下一顆蛋。 如果最後的蛋是藍色的, 就會孵化出酷迪。 紫色的蛋會孵化出杜迪。 紅色的蛋會孵化出法迪。
The incubator currently has 99 eggs in it. 23 are blue, 33 are purple, and 43 are red. You can begin the process of egg fusion by adding an egg of any color to the room. When all the eggs have combined into a single egg, the creature that hatches will bond with you on sight, which is why getting a Cuddly is so important. After all, you made a promise to your son.
目前孵蛋器中有 99 顆蛋, 23 顆藍色、33 顆紫色 43 顆紅色。 你可以放入任何一顆蛋, 啟動蛋融合的過程。 當所有的蛋最終結合成一顆, 孵化出來的生物 看到你的第一眼就跟定你了, 這就是為何得到酷迪會如此重要。 畢竟,你已答應了兒子。
Which color egg should you add to the incubator to get a cuddly?
你應該放入什麼顏色的蛋, 才能得到酷迪呢?
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It’s easy to get mixed up with all the cuddlies, duddlies, and fuddlies coming from different colored eggs. If we ignore how many total eggs of each color there are, and just look at the process of egg fusion, we might notice something that will make this problem simpler.
不同顏色的蛋孵出 酷迪、杜迪和法迪 很容易把人搞糊塗, 如果我們不管每一種 顏色的蛋總共有幾顆, 只去看蛋融合的過程, 我們可能會注意到, 有一種特性能把問題簡化。
When two eggs fuse, the number of eggs of each of those colors decreases by one, and the number of the third color increases by one. That means they all change parity, or evenness and oddness, at the same time. Right now all three piles are odd, but you get to add an egg to one color, which means that it’ll be even and the other two will be odd. Whichever color you choose will always be the opposite parity of the other two piles: odd when they’re even and even when they’re odd, since every egg fusion flips each pile’s parity simultaneously. We want to end with 1 blue, 0 purple, and 0 red eggs, or odd, even, even. That means we want the blue egg pile to be the opposite parity of the other two piles at the start as well.
當兩顆蛋融合時, 兩種顏色的蛋都會少一顆, 第三種顏色的蛋會多一顆。 意味著它們改變了奇偶性, 即奇數、偶數同時都會改變。 目前,三堆蛋都是奇數, 但若給其中一堆加一顆蛋, 這堆蛋會變為偶數, 其他兩堆依然是奇數。 不論你選什麼顏色的蛋, 其奇偶性一定與另外兩堆相反: 另外兩堆是偶數時, 這堆就是奇數,反之亦然, 因為每一次蛋融合就會 讓奇偶性同時調換一次。 我們想最後得到的蛋是一顆藍色、 零顆紫色和紅色,即奇、偶、偶。 也就是說,我們希望在一開始時, 藍色的和另外兩堆奇偶性相反。
So you add a blue egg into the room, and 99 egg fusions later, only a single blue egg remains. The Cuddly that hatches is sure to make your 6-year-old as happy as can be. Just be sure to follow the shopkeeper’s warning, and never feed it after midnight.
所以你只要放入一顆藍色的蛋, 經過 99 次融合之後, 就只會剩下一顆藍色的蛋。 孵化出的酷迪一定 會令你 6 歲的兒子超級開心。 只是一定要遵循店主的警告, 千萬不要在午夜時餵食牠哦。