Tupper's self-referential formula

Quick post today. Let’s implement Tupper's self-referential formula in Racket!

\frac{1}{2} < \left \lfloor mod \left ( \left \lfloor \frac{y}{17} 2^{-17 \lfloor x \rfloor - mod(\lfloor y \rfloor, 2)} \right \rfloor, 2 \right ) \right \rfloor
(tupper 960939379918958884971672962127852754715004339660129306651505519271702802395266424689642842174350718121267153782770623355993237280874144307891325963941337723487857735749823926629715517173716995165232890538221612403238855866184013235585136048828693337902491454229288667081096184496091705183454067827731551705405381627380967602565625016981482083418783163849115590225610003652351370343874461848378737238198224849863465033159410054974700593138339226497249461751545728366702369745461014655997933798537483143786841806593422227898388722980000748404719)

That’s the result of graphing the above function at a point rather far away from the origin. Specifically, where y is around that crazy big number. Look familiar?

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Trigonometric Triangle Trouble

Yesterday’s post at /r/dailyprogrammer managed to pique my interest1:

A triangle on a flat plane is described by its angles and side lengths, and you don’t need all of the angles and side lengths to work out everything about the triangle. (This is the same as last time.) However, this time, the triangle will not necessarily have a right angle. This is where more trigonometry comes in. Break out your trig again, people.

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Crossing hands

Thirty second programming problem from Programming Praxis:

Your task is to write a progam that determines how many times the hands cross in one twelve-hour period, and compute a list of those times.

Ready?

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Factoring factorials

There was a new post on Programming Praxis a few days ago that seemed pretty neat:

Given a positive integer n, compute the prime factorization, including multiplicities, of n! = 1 · 2 · … · n. You should be able to handle very large n, which means that you should not compute the factorial before computing the factors, as the intermediate result will be extremely large.

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Graph coloring

Here’s another one from /r/dailyprogrammer:

… Your goal is to color a map of these regions with two requirements: 1) make sure that each adjacent department do not share a color, so you can clearly distinguish each department, and 2) minimize these numbers of colors.

Essentially, graph coloring.

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Graph radius

Here’s a quick problem from the DailyProgrammer subreddit. Basically, we want to calculate the radius of a graph:

radius(g) = \min\limits_{n_0 \in g} \max\limits_{n_1 \in g} d_g(n_0, n_1)

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