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Can you solve the river crossing riddle?

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    As a wildfire rages through
    the grasslands,
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    three lions and three wildebeests
    flee for their lives.
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    To escape the inferno,
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    the must cross over to the left bank
    of a crocodile-infested river.
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    Fortunately, there happens
    to be a raft nearby.
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    It can carry up to two animals at a time,
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    and needs as least one lion
    or wildebeest on board
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    to row it across the river.
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    There's just one problem.
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    If the lions every outnumber the
    wildebeest on either side of the river,
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    even for a moment,
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    their instincts will kick in,
    and the results won't be pretty.
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    That includes the animals in the boat
    when its on a given side of the river.
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    What's the fast way for all six animals
    to get across
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    without the lions stopping for dinner?
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    Pause here if you want
    to figure it out for yourself.
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    Answer in: 3
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    Answer in: 2
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    Answer in: 1
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    If you feel stuck on a problem like this,
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    try listing all the decisions you can make
    at each point,
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    and the consequences each choice
    leads to.
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    For instance, there are five options
    for who goes across first:
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    one wildebeest
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    one lion.
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    two wildebeest,
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    two lions,
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    or one of each.
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    If one animal goes alone,
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    it will just have to come straight back.
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    And if two wildebeest cross first,
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    the remaining one will immediately
    get eaten.
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    So those options are all out.
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    Sending two lions,
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    or one of each animal,
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    can actually both lead to solutions
    in the same number of moves.
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    For the sake of time,
    we'll focus on the second one.
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    One of each animal crosses.
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    Now, if the wildebeest stays
    and the lion returns,
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    there will be three lions
    on the right bank.
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    Bad news for the two remaining wildebeest.
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    So we need to have the lion
    stay on the left bank
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    and the wildebeest go back to the right.
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    Now we have the same five options,
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    but with one lion
    already on the left bank.
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    If two wildebeest go,
    the one that stays will get eaten,
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    and if one of each animal goes,
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    the wildebeest on the raft
    will be outnumbered
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    as soon as it reached the otherside.
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    So that's a dead end,
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    which means that at the third crossing,
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    only the two lions can go.
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    One gets dropped off,
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    leaving two lions on the left bank.
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    The third lion takes the raft back to
    the right bank
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    where the wildebeest are waiting.
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    What now?
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    Well, since we've got two lions waiting
    on the left bank,
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    the only option is for two wildebeest
    to cross.
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    Next, there's no sense in two wildebeest
    going back,
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    since that just reverses the last step.
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    And if two lions go back,
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    they'll outnumber the wildebeest
    on the right bank.
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    So one lion and one wildebeest
    take the raft back
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    leaving us with one of each animal
    on the left bank
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    and two of each on the right.
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    Again, there's no point in sending
    the lion-wildebeest pair back,
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    so the next trip should be either
    a pair of lions
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    or a pair of wildebeest.
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    If the lions go, they'd eat the wildebeest
    on the left, so they stay,
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    and the two wildebeest cross instead.
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    Now we're quite close because the
    wildebeest are all where they need to be
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    with safety in numbers.
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    All that's left is for that one lion
    to raft back
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    and bring his fellow lions over
    one by one.
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    That makes eleven trips total,
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    the smallest number needed
    to get everyone across safely.
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    The solution that involves sending both
    lions on the first step works similarly,
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    and also takes eleven crossings.
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    The six animals escape unharmed
    from the fire just in time
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    and begin their new lives
    across the river.
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    Of course, now that the danger's passed,
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    it remains to be see how long their
    unlikely alliance will last.
Title:
Can you solve the river crossing riddle?
Speaker:
Lisa Winer
Description:

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Video Language:
English
Team:
closed TED
Project:
TED-Ed
Duration:
04:19

English subtitles

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