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!

The Counterfeit Coin

You are presented with nine gold coins, they appear identical, but you know one of them is not gold, and weighs less than any of the remaining eight coins. You also have at your disposal a balance scale. You are allowed to use the balance scale for two measurements and must correctly identify the counterfeit coin.

Clarification

- A measurement constitutes placement on the scale and observation of balance or lack of balance.
- Your solution must account for all possible results of your first measurement.

Hint and Learning

Did you try to put four coins on each side of the balance scale first? Most people do because this first step seems to accomplish the most work. This is called a hill-climbing heuristic, and although it is great for efficiency it sometimes gets in the way of creativity. Often times, the obvious first step leads to a dead end and the same old results. Next time you are faced with a difficult challenge try exploring alternate first steps and thinking them through. This type of assumption busting should lead to some interesting outcomes and noel results. (Hint: try not starting with four coins on each side)

Solution

Place three coins on either side of the balance, leaving the remaining three coins on the side. If your measurement is in perfect balance, you know the counterfeit must be in the remaining three coins you left on the side. If it is not in balance, then you know the lighter set of three contains the counterfeit coin. So you’ve narrowed it down to three with your first measurement.

Now take two coins from the remaining three and place them on either side of the scale. Either the lighter one is the counterfeit, or if they balance, the coin left on the side is the counterfeit.