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.
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?