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Too Late?

Paul R. McClenon of Washington D.C. contributed this problem to the January-February 1964 issue of Recreational Mathematics Magazine:

The poor patient read the prescription which would save his life. ‘Mix carefully a one-pint drink, made of scotch whisky and water, mixed one to five (1/6 scotch, 5/6 water). Drink it quickly and go to bed.’

However, the patient finds only the following items at hand:

A one-quart bottle, about half full of scotch whisky.
An eight-ounce glass.
An unlimited supply of water from his faucet.
A sink with a drain.
No other containers or measuring devices.

He can pour from either container to the other, without spilling a drop, and can fill either to the brim without loss. How should he mix the prescription? Will he figure it out in time? Will he be saved? Did a doctor or bartender write this prescription?

The magazine went out of business before it could publish the solution. I’ll leave it to you.

05/17/2013 UPDATE: There seem to be a number of ways to accomplish this. Here’s one:

We need a 16-ounce dose that’s 1/6 whiskey, so the final mixture must contain 2.666 ounces of whiskey.

  1. Fill the 8-ounce glass with whiskey, then empty the jug.
  2. Return the glassful of whiskey to the empty jug and add two glassfuls of water.
  3. Fill the glass with this 2-to-1 mixture of water and whiskey. The 8-ounce glass now contains 2.666 ounces of whiskey, our target.
  4. Empty the bottle, pour the glass’ contents into it, and add one 8-ounce glassful of water.

That leaves us with 16 ounces in the jug, 1/6 of which is whiskey and the rest water, as directed.

Thanks to everyone who wrote in.