Yesterday’s Problem:
Which will weigh more – a cubic meter of large steel balls or a cubic meter of small steel balls? Does it make a difference that more small steel balls can be packed into the same space or container than the large steel balls?
Answer:
Whether the steel balls are large or small, packed spheres will occupy about .5235 cubic meters for every cubic meter of space they are packed in. This is independent of the size of the ball, as long as the radius is small in relation to the size of the box.
Even though each void is smaller for tightly packed small spheres, there are more voids altogether. Each box will weigh the same.
Today’s Problem:
I tied some thin thread around a heavy book. As I held both ends of the string. I asked a friend which end would snap when I pulled on the string from the bottom.
If my friend said the upper part, I pulled on the string and the lower part broke. If my friend said the lower part, I pulled on the string and the upper part broke. My friend could never guess the correct answer no matter what choice they offered.
How am I able to achieve this remarkable and quite magical feat?