-
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 as 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?
-
Pause here if you want
to figure it out for yourself.
-
Answer in: 3
-
Answer in: 2
-
Answer in: 1
-
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 lion
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'd 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 eleven trips total,
-
the smallest number needed
to get everyone across safely.
-
The solution that involves sending both
lions on the first step works similarly,
-
and also takes eleven crossings.
-
The six animals escape unharmed
from the fire just in time
-
and begin their new lives
across the river.
-
Of course, now that the danger's passed,
-
it remains to be seen how long their
unlikely alliance will last.