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. 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. 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. 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. Which color egg should you add
to the incubator to get a cuddly? Pause the video to figure it out
for yourself. Answer in 3 Answer in 2 Answer in 1 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. 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. 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.
