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`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? `

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`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. `

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`This is the summation formula for an arithmetic progression that I rediscovered when the need arose.`

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Bingo Pinballs

`Created on 10-17-2017`

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