Puzzles for the Prince of Mathematics

Today is the birthday of “the greatest mathematician since antiquity,” Carl Friedrich Gauss, who was born April 30, 1777.  To celebrate, I am sharing a couple of mind-bending mathematics puzzles.

According to popular lore, Gauss was a mathematical genius since early childhood.  At the age of three, he corrected a math error in his father’s accounts.  At the age of seven, he added the numbers from 1 to 100 in seconds.  (He reasoned that there were 50 pairs that each added to 101.)

Whether these stories are true or not, Gauss attended pre-university at the age of 12 and college at the age of 15.  He pioneered differential geometry, number theory and non-Euclidean geometry.  He also made major contributions in astronomy and physics.  Today, the basic unit of magnetism is the “gauss.”

Now, onto the puzzles.

The first puzzle is from Gauss himself.  When he was 19 years old, Gauss made history by drawing a heptadecagon using only a compass and a straight edge.  A heptadecagon is a regular, 17-sided polygon.  This feat had previously eluded mathematicians for centuries.

Can you do it?

(The mathematical explanation is given in a PDF here, but it may not be understandable without a PhD.  You can view a far more entertaining 2-minute YouTube video demonstration here.)

The second puzzle, while not from Gauss, is a classic math and logic problem.  It recently went viral after being featured in this year’s Singapore and Asian Schools Math Olympiad.

“Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.

• May 15 16 19
• June 17 18
• July 14 16
• August 14 15 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday, respectively.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know, either.

Bernard: At first, I didn’t know when Cheryl’s birthday is, but I know now.

Albert: Then I also know when Cheryl’s birthday is.

So when is Cheryl’s birthday?”

(The answer is discussed here and here.)

Agilent is proud to hire, employ and retain the best and the brightest minds.  Is there an opportunity for you to join our team?  Check out jobs@agilent to find out!