Recreational Math

This page is dedicated to mathematical amusements of all sorts, and to problems I find that are intriguing because they seem counter-intuitive or have an unexpected solution. For example:

Old Boniface he took his cheer,
Then he drilled a hole through a solid sphere -
Clear through the center, straight and strong.
And the hole was just six inches long.
Now, tell us when the end was gained
What volume of the sphere remained?
It sounds like we haven't told enough,
But that's all you need - and it isn't tough!
From "The Surprise Attack in Mathematical Problems", L.A. Graham
See my solution

The Math Puzzler

The puzzler works like this: There is a math question posted below for you to puzzle over. When you have an answer, send it to me in an email. If your answer is right, I'll send you back a code to let you access the next puzzler in the series.

I'll keep extending the series of puzzles as I find or invent new ones, but I'll maintain a list of people who have solved any puzzles, and post a "hall of fame" for those who have solved the most.

Puzzler #1

Prove that 13 + 23 + 33 + ... + n3 = (1 + 2 + 3 + ... + n)2 for all positive integers n.

Submit your answer and your method here. Be sure to include the puzzler number, your name, and your email address.
Enter your secret code to jump to a different puzzler:  

Puzzler Hall of Fame (with number solved so far)

  1. Ibraheem Alolyan (5)
  2. Tom Edgar (1)
  3. Josh Ladd (1)
  4. Hari Aiyer (1)
  5. Bryan Abbe (U. of Mich.) (1)
  6. Joshua Olson (1)