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. Apart from allusions to 42 deliberately introduced by computer scientists for fun and the inevitable encounters with it that crop up when you poke around a bit in history or the world, you might still wonder whether there is anything special about the number from a strictly mathematical point of view. Mathematically Unique? We can also convert by utilizing the inverse value of the conversion factor. In this case 1 inch is equal to 0.06047619047619 × 42 centimeters. 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.

The difficulty appears so daunting that the question “Is n a sum of three cubes?” may be undecidable. In other words, no algorithm, however clever, may be able to process all possible cases. In 1936, for example, Alan Turing showed that no algorithm can solve the halting problem for every possible computer program. But here we are in a readily describable, purely mathematical domain. If we could prove such undecidability, that would be a novelty. For the sum of cubes, some solutions may be surprisingly large, such as the one for 156, which was discovered in 2007: This sum of three cubes puzzle, first set in 1954 at the University of Cambridge and known as the Diophantine Equation x 3+y 3+z 3=k, challenged mathematicians to find solutions for numbers 1-100. With smaller numbers, this type of equation is easier to solve: for example, 29 could be written as 3 3 + 1 3 + 1 3, while 32 is unsolvable. All were eventually solved, or proved unsolvable, using various techniques and supercomputers, except for two numbers: 33 and 42. The problem is stated as follows: What integers n can be written as the sum of three whole-number cubes ( n = a 3 + b 3 + c 3)? And for such integers, how do you find a, b and c ? As a practical matter, the difficulty in making this calculation is that for a given n, the space of the triplets to be considered involves negative integers. This triplet space is therefore infinite, unlike the computation for the sum of squares. For that particular problem, any solution has an absolute value lower than the square root of a given n. Moreover for the sum of squares, we know perfectly well what is possible and impossible. 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:

Inches to centimeters formulae

All this is amusing, but it would be wrong to say that 42 is really anything special mathematically. The numbers 41 and 43, for example, are also elements of many sequences. You can explore the properties of various numbers on Wikipedia. The conjecture that solutions exist for all integers n that are not of the form 9 m + 4 or 9 m + 5 would appear to be confirmed. In 1992 Roger Heath-Brown of the University of Oxford proposed a stronger conjecture stating that there are infinitely many ways to express all possible n’s as the sum of three cubes. The work is far from over. The Gutenberg Bible, the first book printed in Europe, has 42 lines of text per column and is also called the “Forty-Two-Line Bible.”

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 cases of 165, 795 and 906 were also solved recently. For integers below 1,000, only 114, 390, 579, 627, 633, 732, 921 and 975 remain to be solved.The number is the sum of the first three odd powers of two—that is, 2 1 + 2 3 + 2 5 = 42. It is an element in the sequence a( n), which is the sum of n odd powers of 2 for n> 0. The sequence corresponds to entry A020988 in The On-Line Encyclopedia of Integer Sequences (OEIS), created by mathematician Neil Sloane. In base 2, the nth element may be specified by repeating 10 n times (1010 ... 10). The formula for this sequence is a( n) = (2/3)(4 n– 1). As n increases, the density of numbers tends toward zero, which means that the numbers belonging to this list, including 42, are exceptionally rare. Like other computational number theorists who work in arithmetic geometry, he was aware of the “sum of three cubes” problem. And the two had worked together before, helping to build the L-functions and Modular Forms Database (LMFDB), an online atlas of mathematical objects related to what is known as the Langlands Program. “I was thrilled when Andy asked me to join him on this project,” says Sutherland. 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. Ancient Tibet had 42 rulers. Nyatri Tsenpo, who reigned around 127 B.C., was the first. And Langdarma, who ruled from 836 to 842 A.D. (i.e., the 42nd year of the ninth century), was the last.

Forty-two is also a “practical” number, which means that any integer between 1 and 42 is the sum of a subset of its distinct divisors. The first practical numbers are 1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 66 and 72 (sequence A005153 in OEIS). No simple known formula provides the nth element of this sequence. Multiplication Table is an useful table to remember to help you learn multiplication by 42. You should also practice the examples given because the best way to learn is by doing, not memorizing. Online Practice 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.” When I heard the news, it was definitely a fist-pump moment,” says Sutherland. “With these large-scale computations you pour a lot of time and energy into optimizing the implementation, tweaking the parameters, and then testing and retesting the code over weeks and months, never really knowing if all the effort is going to pay off, so it is extremely satisfying when it does.”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. This is another reason I really liked running this computation on Charity Engine — we actually did use a planetary-scale computer to settle a longstanding open question whose answer is 42.”

In other words, the cube of an integer modulo 9 is –1 (= 8), 0 or 1. Adding any three numbers among these numbers gives: The centimeter (symbol: cm) is a unit of length in the metric system. It is also the base unit in the centimeter-gram-second system of units. The centimeter practical unit of length for many everyday measurements. A centimeter is equal to 0.01 (or 1E-2) meter. Centimeters to inches formula and conversion factor

42 Times Tables Chart

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: To calculate an inch value to the corresponding value in centimeters, just multiply the quantity in inches by 2.54 (the conversion factor). Inches to centimeters formulae