Your super-hip firework-fuse cake-timing adventure.

by malmskog

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This whole story was just an excuse to post a picture of fireworks, one of my favorite things. Photo by John Turner, via Wikipedia.

Ah, the joy of the hyphen.  I just learned a lot about compound words and I stand by the hyphenation of this title.  Because this story is about an adventure, which is of a timing nature, specifically the timing of baking a cake, and the timing is accomplished by fuses, specifically those for fireworks, and the fuses are hip, in a way that I would describe as super.  Here’s the story:  You–I ask you to imagine yourself in this adventure–have decided to learn the amazingly hip art of making artisan fuses.  You spin them on some kind of excellent gravity powered spindle, out of the fiber of rooftop-grown cotton, with many essential oils and secret compounds incorporated.  You are supposed to mix all the junk up together, then spin it, and the amount of stuff you have will determine how long it takes the fuse to burn.  So you can measure out the material to make a fuse that will burn for exactly an hour, or exactly two hours, or whatever you want.  However, the fuse that you create will be very non-uniform.  It will burn at a rate that is not perfectly correlated with the length of the fuse.  If you cut an hour long fuse in half, one half might take 10 minutes to burn and the other half 50 minutes.  There’s just no way to tell.

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No, not this kind of Cake.

So, you have plenty of fuses laying around your house.  You decide that you’d like to bake a cake, perhaps to celebrate some amazing math friend’s birthday.  The cake needs to bake for exactly 45 minutes.  Oh darn.  You realize that you have no clock or timer of any kind in your house.  You impulsively threw them all away in an effort to free yourself from THE MAN.  This hasn’t been a problem until now.  With a jolt, you realize that fuses could make excellent timers.  After all, they are each designed to burn for a specific amount of time, right?  You look around the house and find that you have plenty of 30-minute fuses and plenty of 1-hour fuses, but no 45-minute fuses.  This does not seem particularly helpful, though, since you need to time out exactly 45 minutes.  However, I claim that this is actually not a problem.  The question is this–how can you use a 30-minute fuse and a 1-hour fuse to time out exactly 45 minutes?  No cutting is involved.

If you know the answer, you still have time to win a t-shirt!  Just send your answer to mathmostly@gmail.com.  This is your last chance!  Eeek!

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Last week’s puzzle also required you to split the difference.  In that case, you needed to use the fact that the two containers were cylinders.  The key point is that if a cylinder is tilted diagonally so that the syrup just touches the brim and the point where the wall meets the floor, it will be half full.  So, use that technique to get exactly half of each of the containers.  That is, get 3 cups of syrup in the 6 cup container and 2 cups of syrup in the 4 cup container.  Then, pour syrup from the 6 cup container into the 4 cup container until it is full.  This will take 2 of the 3 cups, leaving you with exactly one cup in the 6 cup container.  Brilliant.

Congratulations to Emmie Finkel and Justin Goldman who won this week’s t-shirts!

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