If you use Facebook you will have seen puzzles like the one below. You have to identify the rule that produces the answers in the first 3 lines, and use it to find the result of the fourth line.

 ONLY FOR GENIUSES CLICKBAIT 1 + 4 = 5 2 + 5 = 12 3 + 6 = 21 8 + 11 = ?

However, there are AT LEAST 3 rules that will give correct results for the first 3 lines above, and each gives a different (valid) answer to the 4th line.

How many can you get? You may be able to identify 2 answers, but can you identify three?

All 3 answers involve mathematical solutions. Two of these answers regularly appeared in the replies to the original puzzle. Some assumed a “sequence” and that intermediate “lines” for 4+7, 5+8, 6+9 & 7+10 should be included in the table (inference), others took a stricter “use only the actual evidence” approach (deduction). To stimulate comments clickbate quizzes never indicate whether inference is appropriate (often both methods will provide the same answer).

I didn’t see the 3rd answer although it might appear somewhere amongst the 200K+ comments. This is a blog about contrarian thinking, and for the 3rd solution you will need to approach the problem from a different direction.

 1 + 4 = 5 2 + 5 = 12 3 + 6 = 21 8 + 11 = ?

Answer = 96. Rule: multiply the first and second numbers then add the first number.
So `“8 + 11” = 8 X 11 + 8 = 96`

3 + 6 = 21
8 + 11 = ?
i.e. `8 + 11 + 21 = 40`

The previous answers involved “left side” thinking, you now need to use contrarian “right side” thinking:

 1 + 4 = 5 = 5 2 + 5 = 7 = 12 3 + 6 = 9 = 21 8 + 11 = 19 = ?
i.e. the sums on the left are exactly what they appear to be (“2 + 5” really does mean “2 plus 5”) and what we need is a rule for how the results of the sums are represented on the right side.

In computing (denary) “3” might be represented in Base 2 as “11”, likewise in Quiz Land we can create a rule to represent our results in different Bases. (Online Number Base Calculator here )

1 + 4 = 5 (result represented in Base 6)
2 + 5 = 12 (Base 5)
3 + 6 = 21 (Base 4)
8 + 11 = 201 (Base 3)

So in quiz land our rule is to represent the answer in a Number Base one lower than the previous answer.