Friday, February 22, 2013

Breaking the Space Time Continuum

Time and Space
Part Three
We're breaking out the sand timers and the jugs again as we search for increasingly well composed solutions to measuring puzzles. Then we attempt the theoretically impossible when we try to break the space-time continuum, with toast.

In our adventures in measuring things we've looked at two classical puzzles, The Two Timers and The Two Jugs. Hopefully in exploring the concepts in these puzzles you've started to develop an intrinsic feeling for number.

Just as we look at the properties of words to help us get better at word puzzles, understanding measuring puzzles will really help with all kinds of number problems.

The key to the solutions for all of the jugs and timer puzzles we've examined is learning to consider both what is there, and what is left behind as equally important. The empty spaces in our various glass receptacles proved just as important as what was actually in them. Today we're going to look at a few more puzzles around this theme and see what happens when time and space collide in one of my favourite conceptual physics puzzles - it's about toast!

The Three Jugs - Three, Five and Eight Full

Now things are more complex, although not necessarily more difficult. You have three jugs and as usually they don't have any kind of marking. One of the jugs can hold three units of liquid and the second can hold five units of liquid. The third jug however holds eight units, and is full.

That's all the water you have for this puzzle, eight units. Your task is to split that eight units into two portions of four units using nothing but the jugs.

That shouldn't prove difficult by the way, if you've worked through the previous posts so here's something to think about, can you solve this puzzle for all whole number divisions of the eight units.

The Three Jugs - Four, Seven and Eleven Full

You get the idea by now, can you measure out 1 and 10 units, 2 and 9, 3 and 8, 4 and 7 and finally 5 and 6 units using the four unit, seven unit and full eleven unit jugs?

Now for a devious little trip down memory lane to the sand glasses, and I warn you in advance a timeline will only get you so far. Today we get to play with the four and seven minute timers again.

Wait a minute I hear you cry - along with hurried checking of previous posts - we've already done this puzzle. You're right, you have and I'm sure you worked out that after seven minutes of flipping timers, you can finally time a nine minute duration. Today however your challenge is to break that record.

It's all about finding the most elegant solution, with water jugs we looked for the fewest number of transferals, fillings and emptyings to determine the best solution. Here we are concerned with the up  time. We want to total time needed to set-up our timers and start timing, to be as small as possible.

Sand Timers - Fours and Sevens

You must use the four minute timer and the seven minute timer to time a period of nine minutes once more, but this time you only have a total of nine minutes to do it in, thats right, no set-up time at all.

I make no apology, the answer to this is devious but it does pose the interesting question of how many of our previous answers could have been made more elegant.

OK so when I promised you the breaking of the space-time continuum I may have been exaggerating, but I do have a puzzle which explores space and time; and toast.

Breaking the Toast-Time Continuum

In my kitchen I don't have a toaster, and instead have to rely on a good old fashioned grill, broiler if you use American English. I can toast two pieces of bread at once, and they take 3 minutes a side.

Naturally therefore I can make two slices of toast in six minutes, or for slices in twelve minutes. Unfortunately I like to have three slices of toast in a morning and it irritates me that without breaking the laws of space and time, I stil have to wait 12 minutes. Six to toast the first two slices, and six more to toast the third.

Is there a way to get my toast faster, without destroying physics as we know it, or should I stick to cornflakes?

Here's the solution for Breaking the Toast-Time Continuum, cunning concealed as a video. Be sure to only watch once you have an answer or you're totally stumped and remember to work backwards once you have the answer, see how you could have reached the solution yourself.

For now, with not a dread warning about Cryptic Crosswords in sight, thanks for reading and keep puzzling!

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