Wrong Times Table
Wrong Times Table
[Caption above table:] Wrong Times Table The incorrect answers that feel most right to me


A "times table" (or multiplication table ) is a table used to show the products of numbers. Typically, elementary school children are taught to memorize the table of whole numbers up to 10 as part of learning arithmetic.
In this comic Randall supplies his own alternative version of the multiplication table, with entirely incorrect values that nonetheless "feel" reasonably correct to him. It is unclear how his values are derived, as they don't follow a consistent pattern, but it could be that when calculating products, he sometimes has to correct his mental arithmetic, perhaps thinking along such lines as "8*4 is 36... Or, wait, is it 32?". Most of the values are transposed from their correct position (e.g., adding or subtracting one -- or two, or three -- from one or both multiplicands), some are "off by one" (or two, or by a factor of two), and some (mostly in the 1 row and column) could be created by adding, subtracting, or dividing the two factors instead of multiplying them. It is notable that some properties of mathematics are not followed, as sometimes smaller multiplicands multiply to a larger product than larger multiplicands, and sometimes two even multiplicands produce an odd product.
The table is symmetric, indicating that Randall's form of multiplication is commutative .
The title text (referencing Randall's suspicion that 6x7=42 may be wrong) is an allusion to The Hitchhiker's Guide to the Galaxy , in which the ultimate answer to life, the universe, and everything is said to be forty-two . However, in the book this answer is meaningless without knowing the ultimate question , and so to calculate the ultimate question, a planet-sized computer is constructed. This later becomes Earth, but Earth is destroyed shortly before its calculation is complete. Arthur Dent, one of the last surviving humans, has some white mice (pan-dimensional beings looking like white mice to us) try to get him to give them his brain, so they could attempt to recreate the ultimate question, hoping it may be stored within his brain since he was part of the computer matrix up to just before Earth was destroyed a few days before completing a 10 million year calculation. Arthur refuses, and the mice try to think of some question that makes the answer 42 make sense, like " how many roads must a man walk down ". They also suggest 6x7. Arthur later tries to recreate the question himself by picking letter tiles from a bag, and produces the sentence "What do you get if you multiply six by nine".  This leads him to remark "I always thought something was fundamentally wrong with the universe." Note, however, that operation of said planet-sized computer was disrupted, both by its near-total destruction and by the much earlier crash-landing onto it of the 'B' Ark and its somewhat useless passengers, so it's also possible the universe is okay and only the question was computed incorrectly.  As it happens, 6x9 = 42 in base 13, but Douglas Adams has disclaimed this as being a mere coincidence.  In Randall's table, neither 6x7 nor 6x9 are said to result in 42, but 7x7 is.
If we consider the smaller multiplicand to be a and the larger to be b , then (one of infinitely many possibilities of) the formulas used by Randall are as follows:
The correct multiplication table for the numbers 1-10 is below:
[Caption above table:] Wrong Times Table The incorrect answers that feel most right to me

