Four tramps divide 200 hours of work so that each works a different number of hours a day, for as many days as he works hours a day.

arithmetic/tramps New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

Four tramps divide 200 hours of work so that each works a different
number of hours a day, for as many days as he works hours a day.  How
did they divide up the 200 hours?

This week's challenge comes from an unpublished puzzle book manuscript
from 1895 by two brothers - Clement and Hector fay-ZAHN-dee-ay.  This
puzzle is called "The Tramp's Strategem."  Four tramps applied at a
farmhouse for alms.  "Well," said the farmer.  "I have a piece of work
that will require 200 hours of labor."  And for this work he offered to
pay a specified amount of money for the tramps to divide among
themselves.  The tramps agreed.  But one of them, who was both the
laziest and the smartest of the group, said, "Boys, there's no use in
all four of us doing the same amount of this work.  Let's draw lots for
different amounts.  Each of us will work a different number of hours a
day and each of us will work as many days as he works hours a day.
For example, if a tramp worked three hours a day, he would work three
days at that amount for a total of nine hours."  Well, the plan was
agreed to.  Lots were drawn.  And the lazy tramp made sure that chance
would designate him to work the least amount of time.  And the question
is: How did the four tramps divide up the 200 hours?

-- Will Shortz, NPR "Weekend Edition Sunday", August 28, 1994

Show solution

two, four, six, and twelve

Tramp #1...12 hours for 12 days = 144 hours
Tramp #2...6 hours for 6 days = 36 hours
Tramp #3...4 hours for 4 days = 16 hours
Tramp #4...2 hours for 2 days = 4 hours
              (200 hours total)

That answer assumes that each tramp actually does some work.  If you
disregard that assumption, there's a second answer:

zero, six, eight, and ten

Tramp #1...10 hours for 10 days = 100
Tramp #2...8 hours for 8 days = 64
Tramp #3...6 hours for 6 days = 36
Tramp #4....0 hours for 0 days = 0 hours
              (200 hours total)

-- NPR "Weekend Edition Sunday" puzzle answer, posted by wesun@clark.net,
   September 4, 1994