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.

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 3^{rd} answer although it might appear somewhere amongst the 200K+ comments. This is a blog about contrarian thinking, and for the 3^{rd} 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`

__Answer = 40.__ Rule: add the 2 numbers, then add the result from the previous line

3 + 6 = 21

8 + 11 = ?

i.e. `8 + 11 + 21 = 40`

__Answer 201:__

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 = ? |

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.

You may have found more answers, if so please post them with your explanation in the comments below.

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