Fighting isn’t Pareto Efficient

**Logic!**

Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle with length equal to the distance between strips onto the floor. What is the probability that the needle will lie across a line between two strips?

http://imgur.com/CDCJMce

(note: there is a well-known calculus solution to this problem, but there is also an (extremely hard to see) really cool solution that only uses ratios))

Hover over the below text for hints towards this solution.

HINT

HINT

*The last one (answer at the bottom of my profile)*
Topping Tetrahedral Ten

https://d18l82el6cdm1i.cloudfront.net/image_optimizer/045d0f0e80d52cbe2c1d34aa0a626b0a2a97da0e.jpg

Ten identical spheres are packed as in the above pic. You can either encase the entire stack in a tightly fitting tetrahedron, or you can balance one additional sphere on top. Which will be higher off the ground, the top vertex of the tetrahedron or the top of the additional sphere?

to help with visualization: http://imgur.com/a/iyIVP

Future/Current Forum Game(s)

FGF is dead :(

**Random Stuff for your Amusement**

Graphing like a pro

**My 50 favorite games**

**Quotes:**

I AM FOOD. DESTROYER OF HUNGER.

Actually, y=8/3

“Sir, we’ve been surrounded!”

“Excellent, we can attack in any direction!”

That moment when you fail so much you reflexively push “r” and then suddenly you don’t fail and you’re like yussssshit.

ARE YOU A CAPITALIST?

no, i’m a lowercaseist

**Randomfact(z):**

My first comment has well over 3000 likes.

Started making this profile page actually say stuff in 2014 – 3 years after I became a member. Also the time I started talking on forums and really getting into kong and realizing that, wow, there’s like a actual community and stuff, not just 60,000 people playing games. individually at any given time.

**Goals:**

Respond to 10 shouts left to me by random people (7/10)

**Achievements:**

24000 points. Wow, that’s a lot.

Has a crown on Mozzarella, the coolest kongpanion

1k forum posts: Oct 12, 2014 6:55pm (1277Days)

2k forum posts: Jan 4, 2015 6:51pm ( + 2016 Hours)

5k forum posts: Jun 9, 2015 7:00pm ( + 3744 Hours)

A L33T amount of badges

1 real friend (:

More than 1 real friend 0:

**Forum Games I have hosted**

Feint[Psy Strat]

The Fading Horizon

RESTART

Collapse

Disrupted Rhythm

Limitation II

Don’t Break the Limits

Conquest Complex

FlashFights – Rougelike RP involving a stat based system

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Solution by Leb

Same height: doesn’t matter if you have 10, 4 or only 1 ball, you can cut the pyramid to get the same shape but smaller, inscribing a single sphere. Take triangle ABM, with AB vertices and M the midway point between the other 2, heights and orthocenter H. AB = 1, AM = BM = sqrt(3)/2 (because they’re heights of equilateral triangles), MM’ = sqrt(2)/2 (height of ABM which is isosceles), area(ABM) = sqrt(2)/2, AA’ = sqrt(6)/3 (height), MA’ = sqrt(3)/6 (right triangle, circumradius of MCD), A’H = sqrt(6)/12 (MA’H is proportional to MM’B), so the tetrahedra incircle is exactly 3 times smaller than its circumcircle, qed.