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## Many Worlds Puzzle #3, Solutions

As promised, the solutions…

1.   681472 [Um, Didn’t we answer this one earlier?]

2.   3927.27272… seconds This represents the amount of time it takes the minute hand of a clock to lap the hour hand.  For example, the hands coincide at midnight; they next coincide 3927.27272 seconds later, or at about 1:05:27 AM.

3.   23.14069… This is just e^π.

4.   2.1656 x 10^185 This is how many cubic planck lengths fit in the observable universe…basically, if our universe were a 3D computer, this is how many pixels you’d need.

5.   1.03 light year/year^2 This is the acceleration due to gravity g, in non-standard units.  It has the following interpretation: if you ignored relativity and accelerated at a rate of 1 g (reasonable for a starship), after a year you’d have reached the speed of light.

6.   133956 This is the number of possible combinations of two birthdays, since 133956 = 366^2.  If everyone on Earth had a significant other, there would be over 26,000 couples with the exact same two birthdays as you and your other.

7.   About 19.5 million people The number of people on Earth who share your birthday.

8.   0.739085… This is called the “Dottie number”…an irrational number that solves the equation cos x = x.

9.   1.72048 m^2 The area of a pentagon with sides of 1 m.

10.   0.004295 % This is what percent of Earth’s history homo sapiens has been around.

## Many Worlds Puzzle #3, with HINTS

As promised, here are hints to puzzle #3…

1.   681472 [Um, I did this one as an example?  Do you really need a hint?]

2.   3927.27272… seconds [clocks]

3.   23.14069… [transcendentals]

4.   2.1656 x 10^185 [universe]

5.   1.03 light year/year^2 [Newton’s apple]

6.   133956 [birthdays]

7.   About 19.5 million people [birthdays]

8.   0.739085… [trigonometry]

9.   1.72048 m^2 [area]

10.   0.004295 % [humanity]

Detailed solutions to follow…

## Many Worlds Puzzle #3

Today there are really 10 puzzles. Can you figure out the significance of each number below? I’ve answered the first to get you started.

1.   681472

This number has a prime factorization of 2^9 x 11^3, which indicates that it equals 88^3. There are 88 keys on a piano…so one obvious interpretation is that the number 681472 is the number of possible three-note permutations that could start any piece on a piano (not counting rests, and ignoring duration). I wonder how many of the permutations have actually ever been played over the years?

2.   3927.27272… seconds

3.   23.14069…

4.   2.1656 x 10^185

5.   1.03 light year/year^2

6.   133956