the riddle of the waiter making change — ATOMs #14-8

There is an instructive riddle about a waiter who makes change for a party of three. The total for the meal is $2.50. Daniel Lapin shares it this way:

Each man hands the waiter a dollar bill. On his way back with their change of fifty cents, the enterprising waiter decides that it would be needlessly difficult for the three patrons to divide up the fifty cents, so he pockets $0.20 and hands each man a dime.  Now each man has paid a $1.00 and received back $0.10 in change. So each man really paid $0.90. From all three, the total was $2.70.  The waiter of course has $0.20 in his pocket for a total of $2.90.  The riddle is that since they started with $3.00 but we have accounted only for $2.90, where is the missing dime?

(Daniel Lapin, Thou Shall Prosper. New York: 2002, Wiley.)

Puzzle over this for a moment.  What causes our consternation? We all know that there is no missing dime, but somewhere, in a discourse laden with quantitative details, something is amiss.

I think this is a good illustration of two very important things:

1. Drowning in data. It is far too easy to get off-course when flooded with quantitative details.

2. Two wrongs principle. I won’t revisit the principle here for the sake of time and space, but I will remind the reader that we must carefully examine our assumptions.

(For the record, the erroneous logic was the assumption that “from all three, the total was $2.70” and to this we could add the twenty cents–the fact is, the twenty cents in the waiter’s pocket was part of that $2.70.)

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ATOMs is a monthly column that introduces analytical tools of mathematics and statistics and illustrates their application. To read more about ATOMs, go to the incomplete index, read Where Do We Go From Here, or view the online workbook here.

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