A math prodigy, that's me
When I was a yoot, my math teacher had us do a research project. The topic I fell into was mathematical prodigies. There was a time when they would tour the country and make money doing math shows. I learned that while some were genuine idiot savants, some were charlatans who had learned some nifty math tricks.
We were tasked with giving a presentation, so I of course picked the most amazing trick and got it down pat. I brought in my dad's calculator (calculators were rare, and my dad's was literally the only one around that could display enough digits), and had someone raise a two digit number to the fifth power. Then they'd tell me the number, and I'd tell them the two digit number.
45*45*45*45*45 = 184,528,125
They'd tell me 184,528,125 and I'd tell them 45 after an appropriate pause. Say, 5 seconds. Actually, they'd tell me the number, I'd write it slowly on the chalk board as if I were trying to get it right, then tell them the number right away.
The class tested me again and again. They couldn't believe it. The teacher thought I had a plant, so she worked the calculator herself.
Then she demanded how I did it. I refused to tell her until she'd promised to give me an A. Then I took her out in the hall and told her. The next day she came in and did it.
In the course of my research, I also learned to "cast out nines" and to tell if a three digit number is divisible by 11. This last thing I still do whenever I see a license plate (in Texas, they generally have three digit numbers in them).
BTW, if you want to see the trick, click here. I'm keeping it hidden so that you can think about it before you learn the answer.