Friday, July 11, 2008

Bathroom Monologue: Double and Nothing

There’s an old question of whether you’d like a hundred thousand dollars a month for every month of your life, or if you’d take one dollar for the first month, and have the sum doubled every passing month. The knee-jerk answer is to take the hundred thousand. It’s a lot more than one dollar, or two dollars, or four. On the doubled-dollar option, you’d only receive $2,048 in December (if you began in January).

But a mathematician will tell you that the doubling monthly sum will quickly surpass the hundred thousand. By the end of the second year, your check will be for over eight million dollars. The figure will keep doubling, and the hundred thousand will never catch up. This is what grandfathers have grinned over for generations, while feeding the brainteaser to their know-it-all grandchildren.

But that unlimited wealth proposes an unintended problem. In under four years the recipient will be pulling down over a quadrillion dollars a month. That much money barely exists in the currency of a single nation, meaning they would have to take all the money from everyone else in the country and print more just to hand him his check. This would leave everyone else in poverty, and probably get him killed. If the treasury just printed up the extra few quadrillions for that month, it would so grossly inflate the dollar that the currency would become valueless, again driving everyone else into poverty, and quite probably get our rich man killed.

Because of this terminal flaw in the doubling sum, the meager hundred thousand dollars a month remains the correct answer. It’s good news for the economy, and for all those grandchildren that felt so stupid for not having reached multiplication tables in school.


  1. My grandfather pulled this one on me when I was a kid. Did I want $5 right now or a penny a day to be doubled for a year.

    I fixed his cookies. I took the double. Not because I was a smart kid. I just liked pennies.

  2. Thank you, John. I feel so much better now that I've read your very intelligently reasoned essay. I always knew there was a flaw somewhere...


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