Saturday, February 23, 2013

Turning Back The Sands of Time

Time and Space
Part Four
In our continued quest for elegance in solutions to time and space puzzles we revisit the sand timers with a video and more time lines, explaining just how to get the most elegant of solutions.

In 'Breaking the Space Time Continuum' we revisited the Sand Glass puzzle in search of a more elegant solution. Finding these best-case solution in a common theme in time puzzles, and it usually relies on some clever thinking to find the way of solving them.

In today's video we abandon our timeline method of solving in favour of another visualisation in order to see what we've been missing. Then we revisit the timeline to add our new method of solving to our existing visualisation.

So in order to find these more elegant solutions we have to flip our timers more often. Not only can we flip timers when they run out, we can flip both timers when one runs out. In doing so we get new durations we can time for.

In a sense this is analogous to when we solved The Two Jugs. We are using what is, in effect, the empty space in the timer to time with, instead of the remaining sand, simply by flipping at a known point in the flow.

When timing nine minutes from a four and a seven minute timer we have to follow the following steps.

Flip 4 and 7
Time for 4 minutes leaving (0, 3)
4 Minutes
Flip 4 leaving (4, 3)
Time for 3 minutes leaving (1, 0)
7 Minutes
Flip 7 leaving (1, 7)
Time for 1 minute leaving (0, 6)
8 Minutes
Flip 7 leaving (0, 1)
Time for one minute leaving (0, 0)
9 Minutes

Of course as we saw in the video we can plot these elegant solutions on the time line by changing direction when we flip timers that are not empty but continuing in the same direction when we only flip an empty timer. Here are the most elegant solutions for timing one through twenty minutes shown on the timeline.

So why not try finding more elegant solutions for the three and five minute timers we looked at originally. Some time might also be dedicated to looking at the most elegant times to time a block of durations in succession, so for the first time today I set you a puzzle to which I have no answer - let me know your best solutions in the comments.

Sand Timers - Fours and Sevens

Our fiftieth puzzle is a bit of an epic.

How long does it take to time every round minute duration from one minute to twenty minutes in order?

Any time needed to set up the timers for each duration must be added to your overall duration.

I hope you're enjoying these adventures in time and space as much as I am, and until next time, keep puzzling.

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