Crossing River : 3 Men and 3 Monkeys
Laurie Poon
to cross the river with a fox, a goose and a sack of grain.
Here's a more difficult variation I've heard recently:
Crossing River : 3 Men and 3 Monkeys
====================================
There are 3 men, 2 small monkeys and 1 big monkey on one side of the river.
Beside the river is a row boat, big enough for ONLY two passengers.
The problem is to get all 6 of them to the other side with the following
contraints:
a) Only humans and the big monkey can row the boat.
b) At all times, the number of human on either side of the
river must be GREATER OR EQUAL to the number of monkeys
on THAT side. ( Or else the humans will be eaten by the monkeys!)
This puzzle is best worked out with coins or tokens.
Apologies if this puzzle is old.
What`s in a name?
>Crossing River : 3 Men and 3 Monkeys
>====================================
I've seen this as the Archaeologists and Cannibals puzzle where all the
cannibals can row. It's just a little harder this way.
Spoiler follows:
Since the big monkey can row, a human need not be in the boat at all times,
therefore we give Mr. Big Monkey a workout...
Big Monkey and small monkey row across. Big monkey rows back. big monkey
and another small monkey row across. Big monkey rows back. Two humans row
across.
Take stock:
side 1: Big and one human side 2: two small, two humans, one boat...
We aren't going to change the balance for a while...
Human rows back with small monkey. Human rows across with big monkey.
Human rows back with small monkey.
Now we have:
side 1: two humans, two smalls, and the boat. side 2: one human, one big.
And we are home free... The two humans row across and the big monkey
shuttles the other two monkeys over in two round trips.
--mike
--
Mic3hael Sullivan, Society for the Incurably Pompous
-*-*-*-*-
When I sleep, the world sleeps with me. --Jeremy Radlow
Matt Crawford
) a) Only humans and the big monkey can row the boat.
) b) At all times, the number of human on either side of the
) river must be GREATER OR EQUAL to the number of monkeys
) on THAT side. ( Or else the humans will be eaten by the monkeys!)
This problem cannot be solved exactly as stated. Consider who's in the
boat at any given moment.
(a) One or two humans
Then monkeys outnumber humans on at least one side of the river.
Disallowed.
(b) Two monkeys
One side of the river has 0 or 1 humans. Either the boat just
left from there or the boat is about to arrive there. So the
monkeys either recently did or soon will outnumber humans that on
side.
Disallowed.
(c) One monkey
If humans do not outnumber monkeys on the destination side of
the river, then when the boat arrives, monkeys will outnumber
humans. If humans do outnumber monkeys on the destination side,
then monkeys did outnumber humans on the other side just before
the boat left.
Disallowed.
Thus the boat can only hold one human plus one monkey at all times, and
no progress can be made.
Now if we were to allow there to be N monkeys plus 0 humans together,
then the puzzle could be solved. A solution which makes this assumption
has already been posted.
Ian James Hawthorn
(Matt Crawford) states that the following puzzle is impossible to solve.
... three humans, one big monkey and two small monkeys are to cross a river...
a) Only humans and the big monkey can row the boat.
b) At all times, the number of human on either side of the
river must be GREATER OR EQUAL to the number of monkeys
on THAT side. ( Or else the humans will be eaten by the monkeys!)
Unfortunately Matt Crawfords analysis is flawed - here is a solution.
The three columns represent the left bank, the boat, and the right bank
respectively. The < or > indicates the direction of motion of the boat.
HHHMmm . .
HHHm Mm> .
HHHm <M m
HHH Mm> m
HHH <M mm
HM HH> mm
HM <Hm Hm
Hm HM> Hm
Hm <Hm HM
mm HH> HM
mm <M HHH
m Mm> HHH
m <M HHHm
. Mm> HHHm
. . HHHMmm
In his analysis of the problem Matt Crawford stated -
... if the boat contains ...
>
>(a) One or two humans
> Then monkeys outnumber humans on at least one side of the river.
> Disallowed.
>
>(b) Two monkeys
> One side of the river has 0 or 1 humans. Either the boat just
> left from there or the boat is about to arrive there. So the
> monkeys either recently did or soon will outnumber humans that on
> side.
> Disallowed.
>
>(c) One monkey
> If humans do not outnumber monkeys on the destination side of
> the river, then when the boat arrives, monkeys will outnumber
> humans. If humans do outnumber monkeys on the destination side,
> then monkeys did outnumber humans on the other side just before
> the boat left.
> Disallowed.
>
>Thus the boat can only hold one human plus one monkey at all times, and
>no progress can be made.
>
This reasoning is flawed since monkeys are allowed to outnumber humans in the
case when there are no humans present to be eaten.
Bill Noe
>Unfortunately Matt Crawfords analysis is flawed
>This reasoning is flawed since monkeys are allowed to outnumber humans in the
>case when there are no humans present to be eaten.
I believe the problem here is one of semantics. The problem contradicts itself
by stating the following condition:
> b) At all times, the number of human on either side of the
> river must be GREATER OR EQUAL to the number of monkeys
> on THAT side. ( Or else the humans will be eaten by the monkeys!)
The problem says that the number of humans on one side must ALWAYS be greater
than or equal to the number of monkeys on that side. It implies that this
condition need not be satisfied if there are no humans on one side, but does
not actually say so.
Therefore Matt's estimation of the problem seems to be equally correct. In
fact, he pointed out that given the exception implied by b) above, at least
one solution does exist.
...B
What`s in a name?
>Laurie Poon:
>) b) At all times, the number of human on either side of the
>) river must be GREATER OR EQUAL to the number of monkeys
>) on THAT side. ( Or else the humans will be eaten by the monkeys!)
>
>then the puzzle could be solved. A solution which makes this assumption
>has already been posted.
Oops. You are correct. The puzzle should state that wherever there are
humans, the humans must outnumber the monkeys. (I didn't look closely at
the wording:-()
In this particular case the puzzle is unsolvable.
--mike
l
i
n
e
fodder.
--
Mic3hael Sullivan, Society for the Incurably Pompous
-*-*-*-*-
The reason most folk songs are so atrocious is that they were written by the
people. --Tom Lehrer