My Mathematical Magic Show: Part 9

This mathematical trick was not part of my Pi Day magic show but probably should have been. I first read about this trick in one of Martin Gardner‘s books when I was a teenager, and it’s amazing how impressive this appears when performed. I particularly enjoy stumping my students with this trick, inviting them to figure out how on earth I pull it off.

Here’s a video of the trick, courtesy of Numberphile:

Summarizing, there’s a way of quickly determining x given the value of x^5 if x is a positive integer less than 100:

  • The ones digit of x will be the ones digit of x^5.
  • The tens digit of x can be obtained by listening to how big x^5 is. This requires a bit of memorization (and I agree with the above video that the hardest ones to quickly determine in a magic show are the ones less than 40^5 and the ones that are slightly larger than a billion):
    • 10: At least 10,000.
    • 20: At least 3 million.
    • 30: At least 24 million.
    • 40: At least 100 million.
    • 50: At least 300 million.
    • 60: At least 750 million.
    • 70: At least 1.6 billion.
    • 80: At least 3.2 billion.
    • 90: At least 5.9 billion.








One thought on “My Mathematical Magic Show: Part 9

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.