The Million Dollar Suitcase

Three suitcases are all labeled incorrectly, and you must get the labels right in order to find the million dollar suitcase (the one full of hundred dollar bills).

The labels on the suitcases read as follows:

- $100 Bills
- $1 Bills
- Both ($100 & $1 Bills)

You are allowed one test. You may remove only one bill from a single suitcase, after which you must make your determination. You can’t peek into the suitcases. Can you find the million dollar suitcase?

Can this be done? If so, how? If not, why not?

Hint and Learning

Do you feel like you are missing all the data you need to deduce an answer? Most people do because they don’t take into account that the phrase “Three suitcases are all labeled incorrectly…” provides some really important information about what is not in each suitcase. This lack of clarification is a common pitfall in problem solving - especially creative problem solving. Next time you are faced with a difficult challenge try reviewing all the data and test your assumptions carefully. This can be a powerful method for elucidating the problem or reframing the challenge.

Now go back and try solving the puzzle with this new clarity.

Solution

First, take one bill from the suitcase labeled “Both.” If that bill is a $1 bill, and since all suitcases are mislabeled, then that suitcase must be full of $1 bills.

Since the one labeled “Both” has only $1 bills, that leaves the suitcase labeled “$100 bills” and the suitcase labeled “$1 bills.” Since, all suitcases are mislabeled, the suitcase labeled “$100 Bills” must not have $100 bills in it, and since we’ve already identified the $1 bill suitcase, it must have “Both.” and that leaves the suitcase labeled “$1 Bills,” which must be full of $100 bills (The Million Dollar Suitcase).

If instead that first bill we pulled was a $100 bill, then we found our million dollar suitcase with the first try, woohoo!