## 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.

## Episode 4: This mite be a little fast!

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.

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.