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as a wildfire rages through the
grasslands three lions and three
wildebeest flee for their lives to
escape the inferno they must cross over
to the left bank of a crocodile-infested
River fortunately there happens to be a
raft nearby it can carry up to two
animals at a time and needs at least one
lion or wildebeest on board to row it
across the river there's just one
problem if the Lions ever outnumber the
wildebeest on either side of the river
even for a moment their instincts will
kick in and the results won't be pretty
that includes the animals in the boat
when it's on a given side of the river
what's the fastest way for all six
animals to get across without the Lions
stopping for dinner
if you feel stuck on a problem like this
try listing all the decisions you can
make at each point and the consequences
each choice leads to for instance there
are five options for who goes across
first one wildebeest one lion two
wildebeest two lions or one of each
if one animal goes alone it'll just have
to come straight back and if two
wildebeest cross first the remaining one
will immediately get eaten so those
options are all out sending two lions or
one of each animal can actually both
lead to solutions in the same number of
moves for the sake of time we'll focus
on the second one
one of each animal crosses now if the
wildebeest stays and the lion returns
there will be three Lions on the right
bank bad news for the two remaining
wildebeest so we need to have the Lions
stay on the left bank and the wildebeest
go back to the right now we have the
same five options but with one lion
already on the left bank if two
wildebeest go the one that stays will
get eaten and if one of each animal goes
the wildebeest on the raft will be
outnumbered as soon as it reaches the
other side so that's a dead end which
means that at the third crossing only
the two lions can go one gets dropped
off leaving two lions on the left bank
the third lion takes the raft back to
the right bank where the wildebeest are
waiting what now well since we've got
two Lions waiting on the left bank the
only option is for two wildebeest to
cross next there's no sense in two
wildebeest going back since that just
reverses the last step and if two lions
go back they'll outnumber the wildebeest
on the right bank so one lion and one
wildebeest take the raft back leaving us
with one of each animal on the left bank
and two of each on the right again
there's no point in sending the lion
wildebeest pair back so the next trip
should be either a pair of lions or a
pair of wildebeest if the Lions go they
eat the wildebeest on the left so they
stay and the two wildebeest cross
instead
now we're quite close because the
wildebeest are all where they need to be
with safety in numbers all that's left
is for that one lion to raft back and
bring his fellow Lions over one by one
that makes 11 trips total the smallest
number needed to get everyone across
safely the solution that involves
sending both lions on the first step
work similarly and also takes 11
crossings
the six animals escaped unharmed from
the fire just in time and begin their
new lives across the river of course now
that the dangers past
it remains to be seen how long their
unlikely alliance will last
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