There are two money bags. This first bag contains $10 bills. The second bag is twice as wide, twice as high, and twice as deep as the first, and is totally full of $1 bills. The second bag contains what percentage of the money that the first bag contains?

This classic puzzle plays on our intuition about size and volume. A bag that is twice as big in every dimension isn't just double the size—its volume is actually eight times greater. This is because volume is calculated by multiplying length, width, and height. When you double each of these three dimensions, you are multiplying the original volume by two, then by two again, and then a third time (2 x 2 x 2 = 8). As a result, the second, larger bag can hold eight times as many physical bills as the first one.

Once we know the second bag holds eight times as many bills, we just have to consider their value. Each bill in the large bag is a $1 bill, which is worth only one-tenth of the $10 bills in the first bag. So, while the second bag has eight times the quantity of bills, each bill has only one-tenth the value. This means its total value is eight-tenths (8/10) of the money contained in the first bag.

This type of scaling problem is a great example of the square-cube law. This mathematical principle describes how as an object grows in size, its volume (a three-dimensional measure) increases much faster than its surface area (a two-dimensional measure). The law has profound implications in biology and engineering, explaining everything from why large animals have thicker legs to why crushing a can is easier than pulling it apart.