Booker and Sutherland discussed the algorithmic strategy to be used in the search for a solution to 42. As Booker found with his solution to 33, they knew they didn’t have to resort to trying all of the possibilities for x, y, and z. The answer came in a 2020 preprint, the result of a huge computational effort coordinated by Booker and Andrew Sutherland of the Massachusetts Institute of Technology. Computers participating in the Charity Engine network of personal computers, calculating for the equivalent of more than one million hours, showed:

In the binary system, or base 2, 42 is written as 101010, which is pretty simple and, incidentally, prompted a few fans to hold parties on October 10, 2010 (10/10/10). The reference to base 13 in Adams’s answer requires a more indirect explanation. In one instance, the series suggests that 42 is the answer to the question “What do you get if you multiply six by nine?” That idea seems absurd because 6 x 9 = 54. But in base 13, the number expressed as “42” is equal to (4 x 13) + 2 = 54. The method of using Charity Engine is similar to part of the plot surrounding the number 42 in the "Hitchhiker" novel: After Deep Thought’s answer of 42 proves unsatisfying to the scientists, who don’t know the question it is meant to answer, the supercomputer decides to compute the Ultimate Question by building a supercomputer powered by Earth … in other words, employing a worldwide massively parallel computation platform. The marathon distance of 42.195 kilometers corresponds to the legend of how far the ancient Greek messenger Pheidippides traveled between Marathon and Athens to announce victory over the Persians in 490 B.C. (The fact that the kilometer had not yet been defined at that time only makes the connection all the more astonishing.)

Inches to centimeters formulae

A question that naturally follows is: Is there at least one solution for every nonprohibited value? Computers at Work

The author’s choice of the number 42 has become a fixture of geek culture. It’s at the origin of a multitude of jokes and winks exchanged between initiates. If, for example, you ask your search engine variations of the question “What is the answer to everything?” it will most likely answer “42.” Try it in French or German. You’ll often get the same answer whether you use Google, Qwant, Wolfram Alpha (which specializes in calculating mathematical problems) or the chat bot Web app Cleverbot. An alternative is also that one inch is approximately zero point zero six times forty-two centimeters. Conversion table centimeters to inches chartFor practical purposes we can round our final result to an approximate numerical value. We can say that forty-two centimeters is approximately sixteen point five three five inches: The number 42 also turns up in a whole string of curious coincidences whose significance is probably not worth the effort to figure out. For example: An inch (symbol: in) is a unit of length. It is defined as 1⁄12 of a foot, also is 1⁄36 of a yard. Though traditional standards for the exact length of an inch have varied, it is equal to exactly 25.4 mm. The inch is a popularly used customary unit of length in the United States, Canada, and the United Kingdom. Definition of centimeter

Note that for some integer values of n, the equation n = a 3 + b 3 + c 3 has no solution. Such is the case for all integers n that are expressible as 9 m + 4 or 9 m + 5 for any integer m (e.g., 4, 5, 13, 14, 22, 23). Demonstrating this assertion is straightforward: we use the “modulo 9” (mod 9) calculation, which is equivalent to assuming that 9 = 0 and then manipulating only numbers between 0 and 8 or between −4 and 4. When we do so, we see that: In ancient Egyptian mythology, during the judgment of souls, the dead had to declare before 42 judges that they had not committed any of 42 sins.Sutherland, whose specialty includes massively parallel computations, broke the record in 2017 for the largest Compute Engine cluster, with 580,000 cores on Preemptible Virtual Machines, the largest known high-performance computing cluster to run in the public cloud. An infinite set of solutions is also known for n = 2. It was discovered in 1908 by mathematician A. S. Werebrusov. For any integer p: In 2009, employing a method proposed by Noam Elkies of Harvard University in 2000, German mathematicians Andreas-Stephan Elsenhans and Jörg Jahnel explored all the triplets a, b, c of integers with an absolute value less than 10 14 to find solutions for n between 1 and 1,000. The paper reporting their findings concluded that the question of the existence of a solution for numbers below 1,000 remained open only for 33, 42, 74, 114, 165, 390, 579, 627, 633, 732, 795, 906, 921 and 975. For integers less than 100, just three enigmas remained: 33, 42 and 74. Booker and Sutherland say there are 10 more numbers, from 101-1000, left to be solved, with the next number being 114. To illustrate how difficult it is to find solutions to the equation n = a 3 + b 3 + c 3, let’s see what happens for n = 1 and n = 2.

Deep Thought takes 7.5 million years to calculate the answer to the ultimate question. The characters tasked with getting that answer are disappointed because it is not very useful. Yet, as the computer points out, the question itself was vaguely formulated. To find the correct statement of the query whose answer is 42, the computer will have to build a new version of itself. That, too, will take time. The new version of the computer is Earth. To find out what happens next, you’ll have to read Adams’s books. Since the first such school was created in France in 2013 there has been a proliferation of private computer-training institutions in the “42 Network,” whose name is a clear allusion to Adams’s novels. Today the founding company counts more than 15 campuses in its global network. The number 42 also appears in different forms in the film Spider-Man: Into the Spider-Verse. Many other references and allusions to it can be found, for example, in the Wikipedia entry for “42 (number).” The number 42 is especially significant to fans of science fiction novelist Douglas Adams’ “The Hitchhiker’s Guide to the Galaxy, ” because that number is the answer given by a supercomputer to “the Ultimate Question of Life, the Universe, and Everything.” That calculation is not the only other solution. In 1936 German mathematician Kurt Mahler proposed an infinite number of them. For any integer p:

42 Times Tables Chart

What makes a number particularly interesting or uninteresting is a question that mathematician and psychologist Nicolas Gauvrit, computational natural scientist Hector Zenil and I have studied, starting with an analysis of the sequences in the OEIS. Aside from a theoretical connection to Kolmogorov complexity (which defines the complexity of a number by the length of its minimal description), we have shown that the numbers contained in Sloane’s encyclopedia point to a shared mathematical culture and, consequently, that OEIS is based as much on human preferences as pure mathematical objectivity. Problem of the Sum of Three Cubes Catalan numbers are named after Franco-Belgian mathematician Eugène Charles Catalan (1814–1894), who discovered that c( n) is the number of ways to arrange n pairs of parentheses according to the usual rules for writing them: a parenthesis is never closed before it has been opened, and one can only close it when all the parentheses that were subsequently opened are themselves closed. A team led by Andrew Sutherland of MIT and Andrew Booker of Bristol University has solved the final piece of a famous 65-year old math puzzle with an answer for the most elusive number of all: 42.