Sci Thread Archive from Usenet.com
As youths (16) we played with the 5-cent 25-hole pinball machines in the poolroom. These paid off 5-cents per game that you won. When
you decided to "cash in" your games which of course was a rare event, we called the clerk "Gillie", who had bad eyesight, to come over and
verify the counter, flip the reset switch and pay us the money, which of course went right back into the machine. When we won, Gillie
would come over, squint, and look at the counter. Then he would tell us to flip the switch. In doing so we noticed that the switch could
be toggled back and forth quickly thus stopping the won game count down. So if we had 100 games, we could quickly flip the switch on-and-off to
stop the counter at 99. Then 98 etc. Here in came the problem. If we could trick Gillie to cashing in 100 game, 99 games, 98 etc., How much
money could we win?
That evening I sat with pencil and paper and figured it out by examining a smaller set of numbers and
generalized it to 100(100+1)/2*.05 = $247.5.
This is the summation formula for an arithmetic progression that I rediscovered when the need arose.
Created on 10-17-2017