Math Brain Teaser #7

From Billy-B's legendary 1001 Puzzle Collection — preserved on Puzz.com since 1998.

Puzzle #7

If you started a business in which you earned $1 on the first day, $3 on the second day, $5 on the third day, $7 on the fourth day, & so on, how much would you have earned with this business after 50 years (assuming there are exactly 365 days in every year)?

Reveal Answer

$333,062,500. To begin with, you want to know the total number of days: 365 x 50 = 18250. By experimentation, the following formula can be discovered, & used to determine the amount earned for any particular day: 1 + 2(x-1), with x being the number of the day — The title again holds a hint, although this 1 may have been a bit more obscure. Take half of the 18250 days, & pair them up with the other half in the following way: day 1 with day 18250, day 2 with day 18249, & so on, & you will see that if you add these pairs together, they always equal $36500. Multiply this number by the total number of pairs (9125), & you have the amount you would have earned in 50 years. Except for math gurus (I'm not 1), this puzzle may have proved to be tough. Someone pointed out that a much easier method for solving this problem is squaring the total number of days worked - I like doing things the hard way, though.

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