But slowly, over many years, each value of k was eventually solved for (or proved unsolvable), thanks to sophisticated techniques and modern computers—except the last two, the most difficult of all; 33 and 42. This involves some fairly advanced number theory, using the structure of what we know about number fields to avoid looking in places we don’t need to look,” Sutherland says. This was sort of like Mordell throwing down the gauntlet,” says Sutherland. “The interest in solving this question is not so much for the particular solution, but to better understand how hard these equations are to solve. It’s a benchmark against which we can measure ourselves.”

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 PracticeMost carpet tiles are produced in squares of 50 x 50cm and supplied in boxes of 12. This table will tell you exactly how many tiles you need for a given room size. Simply read off the length and width and where the columns cross, you'll find the answer. What do you do after solving the answer to life, the universe, and everything? If you’re mathematicians Drew Sutherland and Andy Booker, you go for the harder problem. In mathematics, entirely by coincidence, there exists a polynomial equation for which the answer, 42, had similarly eluded mathematicians for decades. The equation x 3+y 3+z 3=k is known as the sum of cubes problem. While seemingly straightforward, the equation becomes exponentially difficult to solve when framed as a “Diophantine equation” — a problem that stipulates that, for any value of k, the values for x, y, and z must each be whole numbers.

And with these almost infinitely improbable numbers, the famous Solutions of the Diophantine Equation (1954) may finally be laid to rest for every value of k from one to 100—even 42. When the sum of cubes equation is framed in this way, for certain values of k, the integer solutions for x, y, and z can grow to enormous numbers. The number space that mathematicians must search across for these numbers is larger still, requiring intricate and massive computations. So, the researchers optimized the algorithm by using mathematical “sieving” techniques to dramatically cut down the space of possible solutions for d. Over the years, mathematicians had managed through various means to solve the equation, either finding a solution or determining that a solution must not exist, for every value of k between 1 and 100 — except for 42. The fact that a third solution to k=3 exists suggests that Heath-Brown’s original conjecture was right and that there are infinitely more solutions beyond this newest one. Heath-Brown also predicts the space between solutions will grow exponentially, along with their searches. For instance, rather than the third solution’s 21-digit values, the fourth solution for x, y, and z will likely involve numbers with a mind-boggling 28 digits.

Tips to memorise the table of 42

For each computer in the network, they are told, ‘your job is to look for d’s whose prime factor falls within this range, subject to some other conditions,’” Sutherland says. “And we had to figure out how to divide the job up into roughly 4 million tasks that would each take about three hours for a computer to complete.”