Bingo Pinballs

This page was created on 9-18-2011


The math-hunters at have a lively discussion, including this excerpt:


Rediscovery is not a silly issue. How many re-discoveries have you made? I would guess many.


As youths (16) we played with the 5 cent 25 hole pinball machines in the pool room. 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.


Based upon that, this is the summation formula for an arithmetic progression that I rediscovered when the need rose………