Uploaded March 2011 | Updated September 2026, 3 weeks ago
Here is a classic, but gory, puzzler of life and death for gnomes. This video comes in three parts, the STATEMENT, a HINT, and the SOLUTION, so pause at the appropriate moments to dwell on the puzzle before I give it all away.
This puzzle appears in chapter 5 of the first volume of THINKING MATHEMATICS, and I also included it in "A Dozen Hat Problems" Math Horizons, April 2009, co-authored with Ezra Brown.
Enjoy!
Here is a classic, but gory, puzzler of life and death for gnomes. This video comes in three parts, the STATEMENT, a HINT, and the SOLUTION, so pause at the appropriate moments to dwell on the puzzle before I give it all away.
This puzzle appears in chapter 5 of the first volume of THINKING MATHEMATICS, and I also included it in "A Dozen Hat Problems" Math Horizons, April 2009, co-authored with Ezra Brown.
Enjoy!





![Fractions take up No Space: Rationals Have Measure Zero (TANTON Mathematics)
How much space do the fractions take up on the number line? NONE!
In this video we add up pieces of ribbon to prove that the fractions have measure zero. It is all very easy and very perturbing because it is easy!
[This video does assume familiarity with the geometric series formula - so you might want to watch a video on that too. I do that with paper tearing!] Fractions take up No Space: Rationals Have Measure Zero (TANTON Mathematics)](https://i.ytimg.com/vi/j2QAhOCdm_o/mqdefault.jpg)




