Nine Coins
Problem, Revisited

Hello! I’M tHe new eDItor oF tHe Puzzles seCtIon. while it’s probably the coolest job at Contingencies, it comes with a lot of pressure. Many of you open each issue expecting a new puzzle that’s neither too easy nor too hard, a puzzle that you haven’t seen before, and, perhaps, a puzzle that calls upon different mathematical abilities from those puzzles published in the past few issues.

For many years I would open Contingencies, go straight to the puzzles page and read it in reverse order. First, to check to see if my name made it to the solver list, then to read the solution to the previous issue’s puzzle, and finally to read the new puzzle (occasionally wondering why the story was so long) and begin pondering whether I would be able to solve it.

Now I can add to this routine the extra pressure of replacing Mark Danburg-Wyld. He did a great job challenging readers of this section for the past five years, and I aspire to reach his competence in combining math and entertainment. Since I’m only starting my tenure as editor, all feedback is welcome (especially positive feedback).

I clearly remember being introduced to the nine coins problem in the second grade: “There are nine coins; one of them is counterfeit and lighter than the real

Solutions may be emailed to
cont.puzzles@gmail.com.
In order to make the solver list,
your solutions must by received
by Jan. 31, 2013.

ones. How does one find the fake coin by using the balance scale two times?” I couldn’t solve it on my own, but the solution was really fascinating, and I didn’t stop thinking about for days (or perhaps weeks). It became a burning reminder that not all solutions are created equal; there are very clever ways of doing things in life, and one should stop and think before tackling a complex problem.

In the spirit of that lesson, here’s a compilation of other, less familiar, weighing problems.

First, there are 10 piles of coins. One
pile contains only fake coins that weigh
nine grams. The other groups contain
only real coins that weigh 10 grams. Us-
ing an electronic scale, what is the least
number of weighings you need to under-
take to determine which pile contains
the fake coins? Note: Unlike the balance
scale, which allows you to compare the
relative weight of two piles, an electron-
ic scale determines the exact weight of
a single pile.