What should I say about this poorly defined question?

Question

If this is a duplicate in any way, I'm sorry; I couldn't find anything.

The Details:

I saw this question on Facebook just now:

If

• $2+3=10,$
• $7+2=63,$
• $6+5=66,$

then $11+12=?$

The intended answer, I suppose, is $253$; the pattern you're supposed to infer is $a+b=a(a+b)$.

The Question:

If you're being pedantic, isn't this problem ill-defined? Can't you get any answer? What should I say about it to educate those answering the question?

Thoughts:

It should be some other binary operation, like $+'$, say, instead of $+$, but the above is how the question is posed. If $2+3=10$, anything follows.

Three values of a binary operation (on, say, $\Bbb N$) isn't enough to pin down other values.

Answer 1

Let's look at this question in a couple of ways.

1. The logical statement 'A implies B' is always true if A is false, so since $2+3$ is not $10$, the answer can be anything.

2. If you are talking about patterns, and take the plus symbol to be some kind of correspondence instead, then the given answer is just one possibility: there is no guarantee that the pattern is indeed $a(a+b)$. Moreover, the plus symbol really shouldn't be used here, because it normally represents normal addition.

I definitely won't set this kind of question in any respectable math exam, though the ability to see patterns is commonly tested in some IQ exam.