How can various combinations of people, animals, and things get across a river when there are restrictions...
decision/crossing/river.crossing Added material
Problem
How can various combinations of people, animals, and things get across a river when there are restrictions on how many can be in the boat, or together on the bank? A fox, a duck, and a bag of corn (or a wolf, a goat, and cabbage) If left alone, the fox will eat the duck and the duck will eat the corn. Only one can fit in the boat in addition to the rower. Three missionaries and three cannibals The cannibals will eat the missionaries if they outnumber them in the boat or on the bank. Only two people can fit in the boat. Missionaries and cannibals again, but only one of each can row (also three humans, one big monkey and two small monkeys) Three jealous husbands and their wives None of the wives can be left in the presence of another man without their husband present. The boat holds two. Two men and one woman row.
Show 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. The fox, the duck, and the corn fdc . . fc d> . fc < d f c> d f <d c d f> c d < fc . d> fc . . fdc Three missionaries and three cannibals mmmccc . . mmcc mc> . mcmc <m c mmm cc> c mmm <c cc mc mm> cc mc <mc mc cc mm> mc cc <c mmm c cc> mmm c <c mmmc . cc> mmmc . . mmmccc Three humans, one big monkey, two small monkeys (Dudeney, Puzzle-Mine, #164) 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 Three jealous husbands and their wives ABCabc . . ACac Bb> . ACac <B b ABC ac> b ABC <a bc Aa BC> bc Aa <Bb Cc ab AB> Cc ab <c ABC b ac> ABC b <B ACac . Bb> ACac . . ABCabc
Additional material
[ Editor: from a mail exchange of September 1997 between Jeff Mackey
and Chris Cole. ]
Jeff Mackey wrote:
> Hi. I'm looking for a puzzle about missionaries and cannibals. It
> goes something like: four missionaries and three cannibals must cross
> a pirrana-laden strem in a canoe that can only hold three at a time.
> If the missionaries are ever outnumbered on any side they get eaten.
> How do they get across? It's obviously a procedural puzzle. The
> wording above is not exact- I seek a correct statement of the riddle
> and a solution. I think I have an interesting methodology for
> solving it, but obviously I need it correctly posed to do so.
>
> Scientific American had a great graphical solution to the problem,
> perhaps 30 years ago. If you have any leads, like what issue it was
> in, I'd appreciate that.
Three missionaries and three cannibals have to cross a river. None can
swim and they must cross using a small boat that carries only two
persons. All of the missionaries can operate the boat but only one of
the cannibals can. A missionary can be alone with a cannibal but if
one missionary is left with two cannibals the missionary will be
killed. How can they all get safely across the river?
I use capital letters for boat drivers, and '*' to represent the boat.
left bank right bank
0. Initial position: MMMCcc*
1. Two cannibals go over MMMc *Cc
2. Cannibal comes back MMMCc* c
3. Two cannibals go over MMM *Ccc
4. Cannibal comes back MMMC* cc
5. Two missionaries go over MC *MMcc
6. Missionary & cannibal come back MMCc* Mc
7. Missionary & CANNIBAL go over Mc *MMCc
8. Missionary & cannibal come back MMcc* MC
9. Two missionaries go over cc *MMMC
10. Cannibal comes back Ccc* MMM
11. Two cannibals go over c *MMMCc
12. Cannibal comes back Cc* MMMc
-- Chris Cole <chris@questrel.com>
[ Editor: the collected copy of the mail ends at step 12; one more
crossing, of the two cannibals on the left bank, completes it. No
solution of Mackey's four-missionary version was collected. ]