Episode 4: This mite be a little fast!

The mite turns
The mite Paratarsotomus macropalpis is faster than any other animal on earth… (for its size), and it turns using its limbs like grappling hooks. Look at that!

Episode 4 is up! The Recent Paper is:

Rubin, S., M. Ho-Yan Young, J. C. Wright, D. L. Whitaker, and A. N. Ahn. 2016. Exceptional running and turning performance in a mite. Journal of Experimental Biology 219:676-685.

Eight-legged mites move four limbs at a time.
Eight-legged mites move four limbs forward all at the same time, while the other eight stay planted. Then they do the opposite. Etc.

And the Decent Puzzle is called “Roll of Tape.”

Puzzle 3: Hints

This puzzle appears in episode 3, and it’s about a chess board. 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.

    • Count how many squares fit in a 1×1 grid, then 2×2, then 3×3. Is there a pattern?
    • Does your pattern give the right answer for an 8×8 grid (204)?
    • From there you can bust out a calculator, or find an equation for the sum of squares
    • Oh… that equation is tot = n·(n+1)(2n+1)/6

The answer to puzzle 3 is in Episode 4.

Puzzle 2: Hints

This puzzle appears in episode 2, and it’s about compound interest. 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 working on a puzzle.

  • There is a mathematical formula for compound interest, paid at the end of each year
  • That formula is: A=P·(1+r)^n, where…
    A=money you get at the end of the term;
    P=Principal at beginning of the term;
    r= interest rate (i.e. 1% interest would be r = 0.01);
    and n=number of years for which compound interest accrues.
    For example, $100,000 at 1% for 10 years = $100,000·(1+.01)^10 = $110,462.21
  • You can plug real numbers into that equation to get the answer, but… if you like algebra, rewrite the equation to take the two separate 10-year terms into account
  • That gives you:  A = P · (1+r1)^n1 · (1+r2)^n2
  • What happens to that equation when you swap the first and second terms?

The answer to puzzle 2 is in Episode 3.

Puzzle 1: Hints

Our first puzzle appears in Episode 1. 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 working on a puzzle.

  • Think of a triangle with endpoints at the centers of all three coins.
  • What’s its area?
  • What’s the area of a circle?
  • What’s a 6th of that?
  • Can you recreate the shape in question by adding and subtracting areas?

The answer to puzzle 1 is in Episode 2.

Episode 1: New 9th Planet

The white circle at the center of this image is our solar system, out to Neptune. The proposed new planet's orbit is the huge orange one on the right side.
The white circle at the center of this image is our solar system, out to Neptune. The proposed new planet’s orbit is the huge orange ellipse on the right side. Image Credit: Caltech/R. Hurt.

Episode 1 is up! The Recent Paper is:

Batygin, K. and M. E. Brown. 2016. Evidence for a distant giant planet in the solar system. The Astronomical Journal 151(2).

And the Decent Puzzle is called “The Three Coins.” Hints will be posted 24 hours after this one, and the solution will be part of the next podcast episode.