Logistics for Missionaries

We’ve all heard the one about the guy with a fox, a chicken, and a bag of chicken feed who wants to cross a river in a canoe, but can only carry two of the three with him at once. It led me to consider the following scenario only Latter-Day Saints can appreciate:

Consider 8 missionaries comprising a district. The 6 Elders and 2 Sisters have just met together at a chapel for a district meeting and now they want to travel 10 miles across town to the LDS Temple. The district shares two cars, but doesn’t have any bicycles (assume transit is not an option). How should the district minimize the number of miles (scarce resource) used transporting all 8 missionaries? Each car may legally hold 5 missionaries. Assume all missionaries follow all mission rules. Companionships need not stay together, but all missionaries must have a companion, and sisters may not be companions with elders. Elders and Sisters are not permitted to ride in cars together. Two elders must not be left in any location with two sisters (3 or more elders may be left alone with 2 sisters). Assume that all missionaries must either be at either the Chapel, the Temple, or in direct transit between the two.

Being an engineer and all, I feel like I should be able to arrive at a good solution, but my best option requires no less than 60 miles. Can anyone beat this?

How would your solution change if the objective were to minimize total person-miles traveled rather than total vehicle-miles traveled? (mine requires 160 person-miles)

1 comment to Logistics for Missionaries

  • curtis

    I think 60 miles is as good as it gets.
    Here’s my solution:

    4 elders take one car, leaving 2 elders behind.
    2 sisters leave at the same time in the 2nd car.
    2 elders are dropped off at the temple, and 2 return to the chapel.
    Since the sisters can’t be alone with the 2 elders, they have to return to the chapel in their car.
    The 2 elders pick up the remaining 2 elders and both cars return to the temple.

    The sisters are basically making an extra round trip to avoid being at either end with 2 elders. A better strategy is for the sisters to stop for ice cream to kill time while the elders ferry themselves to the temple. Result: 40 miles, no broken rules, plus ice cream.