Missionaries and Cannibals
On the left bank of a river, there are 3 missionaries and 3 cannibals. The goal is to safely get the 6 people to the other side under the following constraints: They have a row-boat which holds up to 2 occupants. At no time can there be more cannibals than missionaries, or lunch will be served. Problem: Defining a crossing as a traverse across the river one way, how many c crossings will be required?
Solution; For brevity, we give the number of missionaries(M) and cannibals(C) on each side after each crossing.
Start: on left,MMMCCC, on right, no one. After 1st crossing, on left, MMMC, on right, CC. After2nd crossing, on left,MMMCC,
on right, C After 3rd crossing, on left,MMM, on right, CCC. After 4th crossing,on left,MMMC, on right CC. After 5th crossing,
on left ,MC, on right, MMCC. After 6th crossing, on left MMCC, on right, MC.After 7th crossing, on left CC, on right, MMMC.
After 8th crossing, on left, CCC, on right, MMM.After 9th crossing, on left, C, on right, MMMCC. After 10th crossing, on left,
CC, on right, MMMC. After 11th crossing, on left, no one, on right, MMMCCC. Everybody is hungry.
The answer is 11.
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1 solution
Solution; For brevity, we give the number of missionaries(M) and cannibals(C) on each side after each crossing. Start: on left,MMMCCC, on right, no one. After 1st crossing, on left, MMMC, on right, CC. After2nd crossing, on left,MMMCC,
on right, C After 3rd crossing, on left,MMM, on right, CCC. After 4th crossing,on left,MMMC, on right CC. After 5th crossing,
on left ,MC, on right, MMCC. After 6th crossing, on left MMCC, on right, MC.After 7th crossing, on left CC, on right, MMMC.
After 8th crossing, on left, CCC, on right, MMM.After 9th crossing, on left, C, on right, MMMCC. After 10th crossing, on left,
CC, on right, MMMC. After 11th crossing, on left, no one, on right, MMMCCC. Everybody is hungry.