re: Bizarre Math Question and Answer breaks the internet - Sorry if already posted

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You're making an additional assumption by solving the 2(9+3). Pretending things exist that don't is not the most "rational" solution. As explicitly stated that answer is 288. Therefore, fewer assumptions = more logical approach.


2(9+3) isn't explicit multiplication, it is multiplication by juxtaposition which is the exact same thing as 2X and no one would solve that as 2*X.

There isn't implied parenthesis, the argument is that multiplication by juxtaposition always takes precedence.

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Here is the professor from Cal-Berkeley--who is arguing that both 2 and 288 are correct--has to say about Multiplication by Juxtaposition.

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Finally, the convention in algebra of denoting multiplication by juxtaposition (putting symbols side by side), without any multiplication symbol between them, has the effect that one sees something like ab as a single unit, so that it is natural to interpret ab+c or a+bc as a sum in which one of the summands is the product ab or bc. Without that typographic convention, the order-of-operations convention might never have evolved. When one has numbers rather than letters, one can't use juxtaposition, since it would give the appearance of a single decimal number, so one must insert a symbol such as ×, and there is less natural reason for interpreting 2 × 3 + 4 as (2 × 3) + 4 rather than 2 × (3 + 4), but I suppose that we do so by extension of the convention that arose in the algebraic context. Likewise, because addition and subtraction constitute one "family" of operations, and multiplication and division another, and perhaps also because the slant "/" doesn't seem to separate two expressions as much as a + or - does, we are ready to read a/b+c etc. as involving division before addition. But when it comes to a/bc, where the operations belong to the same family, the left-to-right order suggests doing the division first, while the "unseparated letters" notation suggests doing the multiplication first; so neither choice is obvious.

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As he says, the non-algebraic representation makes one way or the other less clear. Furthermore, the best I can tell, there isn't clear consensus on whether it always takes precedence anyways.

I say though that, given the syntax, it is best to limit assumptions, and solve as presented, which would result in 288.