How to answer a question when you don’t even know the question!

Sometimes you can answer multiple-choice questions using game theory even if you don’t know the question!

Imagine you are sitting an SAT test and the possible answers are:

A. 5 – 2√6
B. 5 – √6
C. 1 – 2√6
D. 1 – √2
E. 1

With no more information we can have a good guess at the answer, as long as we put ourselves in the shoes of the test setter.

The aim of the test setter is to give answers that are at least reasonable to people trying to take the test. We can see that the square root of 6 (which is written as √6) appears in three of the answers. It would be very odd for someone setting the test to include an obscure number in three of the five answers without it being part of the answer. So it is reasonable to guess that √6 is probably part of the answer, so we rule out answers D and E.

We can now see that of the three remaining answers 2√6 appears in two: A and C, and 5 appears in two A and B. Once again the question setter is going to put in elements of the answer which look reasonable to the person taking the test so we now guess that both 5 and 2√6 are part of the answer.

The only answer that contains both of these elements is A, so we can take a good guess that this is the answer.

It is indeed the answer, the question is what is ( √2 – √3 )² equal to and appears as question 7 on this sample SAT test.

Today’s takeaway: Putting yourself in the other person’s shoes can be a powerful way to solve problems

Avinash Dixit and Barry Nalebuff give a similar example in their book:

The Art of Strategy: A Game Theorist’s Guide to Success in Business and Life

Their example and explanation is quoted here by Freakonomics.

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