Can you solve the river crossing riddle? - Lisa Winer
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.
