Practical Puzzles

My friend and previous roommate, Ramin, always enjoyed practical science puzzles, that is, puzzles that we find in real life requiring only basic science. Inspired by this, here are a few that might catch your interest. If you think you have a solution but want to check it, send it to me by email at: Mark.Moyer@uvm.edu. Likewise, if you have an interesting puzzle yourself, send it to me and I'll possibly add it to the list.

Solved Puzzles

• Man-Hole Covers
  Why are man-hole covers round? (One answer supposedly stands out above the others.)
  The stories I've heard say this question was given at several Ph.D. qualifying exams at Stanford.
• Man-Hole Covers II (for after you've solved the above puzzle)
  What other man-hole cover shapes would be equally good according to the above reasoning (i.e. from the first puzzle)? Can you name another? Several others? Can you characterize the class of qualifying shapes mathematically?
• Mirror Images
  As we all know, a mirror reverses an image. For example, ambulances often write "Ambulance" backwards across the front of the ambulance so people can read it in their rear-view mirrors. But why do mirrors switch left-right and not top-bottom? Why do ambulances write "Ambulance" backwards rather than upside-down? (This is Ramin's puzzle.)
• Seeing With Glasses
  People who are far-sighted can see things in the distance normally but can't see things that are very near. People who are near-sighted can see things that are very near normally but can't see things in the distance very well. If a near-sighted person wears corrective lenses, she will be able to see both things that are near and things that are far. If a far-sighted person wears corrective lenses, he will be able to see things that are very near but will be unable to see things that are far away. Why the difference? (This is a puzzle my wife thought up.)
• Astronomical Anomalies
  The days vary in length depending on the season, as we all know. One would expect that at the summer solstice, the sun rises the earliest and sets the latest, making it the longest day of the year. But if you consult the astronomical charts, the longest day of the year, the day with the earliest sunrise, and the day with the latest sunset are three different days, falling a few days apart from each other. Explain.
• Seeing Through the Mist
  Every morning I make oatmeal. I boil the water, add the oats, stir them for a few minutes, and then turn off the burner before adding banana slices and serving. As I stir the boiling oats, I see steam rising from the pan, as one would expect. However, when I turn the burner off, the amount of steam rising from the oats increases quite noticeably (try it yourself!). Explain.

Unsolved Puzzles

• All Wet
  Many things turn darker in color when they get wet -- clothing, sponges, wood, cement, and even rocks. Why? (Another of Ramin's puzzles.)
• Tree Wells
  Often in winter, you'll see that the snow isn't as deep around trees. There are 'tree wells' that extend out from the tree for 6"-24" and can be of about any depth. But why isn't the snow as deep around trees? That is, why are there tree wells? (A quick google search turns up a few different answers, but the one I assume is correct isn't explained very thoroughly.)
• Too Spicy?
  My wife and I both enjoy fairly spicy foods. But of course there are limits. What I find strange is that some dishes seem too spicy to me and not that spicy at all to her while other dishes are too spicy for her and not that spicy to me. Why?

Impractical Puzzles

• When was I born?
  Web pages are often so impersonal, so I thought I'd reveal my age with a puzzle.

  There is an ordered list L of numbers such that:
  a) all the numbers are primes,
  b) if we compare any number on the list and the next number on the list the latter is between 2 and 3 times the former,
  c) each of the numbers is on exactly one of three other lists, D, M, and Y (and these lists consist only of numbers from list L), such that the product of all the numbers on list D is the date of my birth, the product of all the numbers on list M is the month of my birth, and the product of all the numbers on list Y is the year (four digits) of my birth.

  When was I born?

  Unfortunately, you don't have enough information. So perhaps I should tell you what the sum of all the numbers on list L is. That would definitely give you enough information. But wait a minute -- you already have enough information!

  When was I born?

For Philosophers

• Which philosopher said the following (quote taken out of context)?
  I think philosophy cannot credibly challenge either the positive convictions of common sense or the established theses of the natural sciences and mathematics.
  Solution.

Puzzles/Contests