Cluemeister's Corner

January Puzzle: Sands of Time

On New Year's Eve, a time when all eyes are drawn to the calendar and the clock, precision to the second can be important even those for those celebrants whose occupations demand no precision. As we enjoy the sunny-side-up resolutions that comprise our January breakfast, allow the Cluemeister to present a poser concerning that device which allows us our precisely cooked dishes: the timer.

The Cluemeister speaks not of oven timers or mechanical timers, but sand timers, used for cooking eggs and percolating games of Boggle alike. Numberless and simple, they can be a challenge to use precisely.

Imagine that you possess two hourglass-style sand timers, identical but for the widths of their waists. The one measures M minutes, the other N minutes, but what you need is a way to measure 8 minutes, to the nearest second. Merely eyeballing quantities of sand will not be precise enough. And of course, you possess no other time-telling devices.

How can you use these two timers to measure a period of exactly 8 minutes if...

A) M is 13 and N is 6?

B) M is 9 and N is 6? (M was originally given as 3 here--the Cluemeister apologizes for the error.)

C) M is 32 and N is 64?

While a three-part answer is ideal, solutions for some but not all parts will be cheerfully accepted. (Solutions for no parts will be gazed upon in zen-like wonder.) Feel free to be creative, but not too creative. Send answers to thorin (dot) tatge (at) pobox (dot) com until January 29th.