Solution to Puzzle 008

In episode 8 we gave a puzzle called “the square post.” If you want to hear the puzzle again, you listen to the episode here, and skip to 8:20 or so.

Listener Evan Brock has come through like a champ with a nice visual solution. If you’re stuck, or want to compare your methodology with someone else’s, have a look!

RP-DP-008 Solution

Thanks, Evan!

 

Episode 8: Air Rage and Class Warfare

The mere sight of this spread on the way to your crap seat at the back of the plane might be enough to make you snap.
The mere sight of this spread on the way to your crap seat at the back of the plane might be enough to make you snap.

Episode 8 is up! The recent paper is:

DeCelles, K. A., and M. I. Norton. 2016. Physical and situational inequality on airplanes predicts air rage.  Proceedings of the National Academy of Sciences of the USA doi: 10.1073/pnas.1521727113.

And the decent puzzle is called “The Square Post.”

Puzzle 6: Hints

This puzzle appears in episode 6, and it’s about a dice game called “singles, doubles, triples.” Select the text below if you want to read a hint.

Try selecting the first bullet point alone, see if that helps. If not, select the first two, etc. The answer isn’t really important. The whole point is to enjoy the process of doing a puzzle.

  • I made an excel spreadsheet to tackle this one. There are 6*6*6=216 possible rolls of three dice, each of which happen with equal probability. For each, I categorized it as single (all three dice are different), double (one matching pair among the three dice), or triple (all three dice are alike). And for each I calculated the product of the three dice.
  • 120/216 were singles, and the total for all of those was 4,410.
  • 90/216 were doubles, and the total for all of those was also 4,410. I was shocked. SHOCKED! That these were equal! There must be a reason. Or is it a fluke? I don’t know. Moving on…
  • 6/216 were triples, and the total for all of those was 441. Weird, right? Exactly one tenth of the other ones? What the hell?
  • So if you multiply all scores for the triples by ten, everything evens out, and the odds are equal for everyone.
  • I have to say…. the symmetry of this blows my mind..

The answer to puzzle 6 is in Episode 7.

Puzzle 5: Hints

This puzzle appears in episode 5, and it’s about a hollow cube. Select the text below if you want to read a hint.

Try selecting the first bullet point alone, see if that helps. If not, select the first two, etc. The answer isn’t really important. The whole point is to enjoy the process of doing a puzzle.

  • The outer area and the inner area can both be expressed as a function of the length of one side of the cube.
  • Let’s call the length of a side x. Each face has an area of x*x, or x^2. There are six sides. So the total outer area is 6·x^2.
  • Each inner face has the same area as an outer face, but with one ring of tiles removed all the way around. Instead of each face having an area of x^2, it has an area of (x-2)^2. So the total for all six sides is just 6·(x-2)^2
  • the difference between the inner and outer area, then, is 6x^2 – 6·(x-2)^2.
  • You are looking for a solution for x, such that 6x^2 – 6·(x-2)^2 = 600. At this point it’s algebra.

The answer to puzzle 5 is in Episode 6.

Puzzle 4: Hints

This puzzle appears in episode 4, and it’s about a roll of tape. Select the text below if you want to read a hint.

Try selecting the first bullet point alone, see if that helps. If not, select the first two, etc. The answer isn’t really important. The whole point is to enjoy the process of doing a puzzle.

  • There are many ways to come at this one. I thought about it in terms of conservation of mass – when it’s unrolled, it should have the same volume as when it’s rolled up.
  • Truth be told, you can ignore one dimension altogether, so maybe just draw the rolled up tape as a circle, and draw the unrolled tape as seen from the side, as a very flat, long rectangle.
  • The area of the circle and the rectangle should be the same, no?
  • The area of a circle is pi·r^2, and the area of the rectangle is height * length.
  • In other words, pi·(diameter/2)^2=(thickness)(length). Solve for length.

The answer to puzzle 4 is in Episode 5.