Every so often, I’ll informally teach a class of gifted elementary-school students. I greatly enjoy interacting with them, and I especially enjoy the questions they pose. Often these children pose questions that no one else will think about, and answering these questions requires a surprising depth of mathematical knowledge.
Here’s a question I once received:
255/256 to what power is equal to 1/2? And please don’t use a calculator.
Answering this question is pretty straightforward using algebra:
However, doing this without a calculator — and thus maintaining my image in front of these elementary school students — is a little formidable.
I’ll reveal how I did this — getting the answer correct to the nearest integer — in tomorrow’s post. In the meantime, I’ll leave a thought bubble if you’d like to think about it on your own.