The Nugget Puzzle: Don’t Dilute The Cabernet. On a table before you are
two 12 oz glasses. In the first (A) we have 10 oz of Cabernet. In the 2nd (B)
someone has poured 10 oz of (ugh) water. In an act of disgusting perversity, 1
oz of the wine is poured into the water. Cabernet lovers, in an attempt to
recoup their losses, vainly pour 1 oz of the thoroughly stirred mixture of
glass B into glass A. Your Nuggetory Problem: Which glass now contains
the purest mixture relative to its original content (A having been being
100% wine and B originally containing 100% pure water). Note: wine and water
are entirely different materials for this exercise. As usual, No Tricks.
While there is a temptation to break out your best fraction protocol for this
problem, forget it – there’s a much better way.
The beauty of this puzzle is that it offers a novel way of thinking about such
matters leading to quick and almost math-less solution.
Without bothering with calculations, just assume an amount of water that’s
in the wine at the end of the exchanges. Let’s say that there’s 1 ounce of
water in the glass originally containing pure wine. That means the wine is
now 90% pure (9 ounces of wine, 1 ounce water).
Now turn your attention to the other glass which was originally filled with
10 ounces of water. It now has 9 ounces of water (the missing ounce is in
the wine) so the rest is wine, giving it a 90% purity rating relative to its
original composition. No matter what number you assume, the percentages
will always be the same!
Repeat the exchanges a 1000 times and you will find the percentages of
original material is always equal in the two vessels (ultimately converging to
50% purity).
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