Solution to: Cash for a Car

Unfortunately, Lucas Jones didn't provide a more elaborate explanation. But thanks to Ronald A. Laski we can now present a more acceptable explanation:

In Envelope #14, there are:

    81 $100 bills = $8100
     1 $ 50 bill  = $  50
     2 $ 20 bills = $  40
     1 $  2 bill  = $   2
                    ----- +
                    $8192 (total amount of money for Envelope #14)

     1 $100 bill  = $100
     1 $ 20 bill  = $ 20
     1 $  5 bill  = $  5
     1 $  2 bill  = $  2
     1 $  1 bill  = $  1 <- that's the one!
                    ----
                    $128 (total amount of money for Envelope #8)

Envelope #2 has 1 $2 bill in it, which is its total amount also.

Now $8192 + $128 + $2 = $8322. And that is the winning bid!
The amount of money in each envelope is 2 ^ (# of envelope - 1), except for envelope 15, which contains $8617.

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