Happy 100! A Celebration with Puzzles and More

WOOT!  Today celebrates my 100th post for the Agilent Technologies Blog, which I started writing just about a year ago.  To honor this milestone, I present some fun facts and puzzles about “100.”

  • 100 is the exact sum of the first nine prime numbers (2, 3, 5, 7, 11, 13, 17, 19 and 23).
  • 100 is also the exact sum of the cubes of the first four integers (13 + 23 + 33 + 43).
  • Amazingly, 100 also equals the square of the sum of the first four integers (1+2+3+4)2.
  • The word “hundred” didn’t always refer to a quantity of 100. It used to refer to a quantity of 120, and in some cases 2,880.

Now, onto the puzzles.  (The last two are rather morbid in their original versions; I toned them down for sharing with your friends and family.)

(1)

What is the sum of the first 100 natural numbers (1 through 100)? Now, how fast can you figure this out?  The mathematician Carl Frederick Gauss was able to solve it immediately – and ingeniously – when he was only five years old.  (Answer)

(2)

Using standard mathematical operations and brackets [+, -, x, ÷, (, )], can you arrange the numerals 1, 7, 7, 7 and 7 (one 1 and four 7s) into an equation that equals 100? (Two answers)

(3)

100 people stand in a single-file line, each facing forward, and given a red or blue hat at random. Each person can see the hats of everyone in front of them, but cannot see their own hat.  Beginning with the person at the back of the line, each person is allowed to guess the color of their own hat.  They may say only one word: either “red” or “blue.”

The team is freely allowed to discuss strategy before the exercise begins.  What plan can you develop that enables the maximum number of people to guess correctly?  The possible number is much higher than you may think!  Note: there is no “trick” to this problem or its solution.  The number of red and blue hats is completely random.  (Hint) (Answer)

(4)

100 people stand in a circle. No. 1, designated “it,” taps the next clockwise person (No. 2), who is eliminated and steps out of the circle.  The next clockwise person (No. 3) becomes “it” and repeats the process.  The game continues until only one person is left.  What number is that person?  (Answer)

Agilent has two products named “100.”  The Agilent 100 Automated Disintegration Apparatus measures how long it takes a sample to disintegrate into particles for compliance testing.  The Cary 100 UV-Vis is a system for molecular spectroscopy.


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