Murphy Choy

Archive for August, 2011|Monthly archive page

A simple question that is plainly confusing.

In Uncategorized on August 6, 2011 at 8:15 am

This is actually a post not on analytics but on the problem of improper framing of questions.

This question came from one of my online contacts who claims this is a question for 7 years olds. Let us see the combination of the question.

As described by him,

5 men met at a party, they give each handshake. How many handshakes are there altogether?

Interesting way of describing question. But there are several issues with this framing of the question.

  1. It is not obvious whether the hand shakes are unique or not.
  2. It is not obvious that whether who is giving the hand shakes.

Why the problems? They all give different solutions.

The first problem is a permutation problem and the second is a reference problem.

The first problem will yield two answers, 10 and 20. How so?

If you are supposed to shake hands with people who you have not shake hands with, then the first person shakes 4 hands, the second person shakes 3 hands, the third person shakes 2 hands and the fourth person shakes 1 hand. The total number of hands is 10.

However, if this is not the case, as in some formal settings where everyone has to shake everyone’s hand (typically a communal setting or gift exchanges), you may have to shake the hands of someone who has shake your hands before multiple times. Then everyone has 4 hands to shake, that is 20 hands.

In the last case where it is to a reference point, then only 5 hands are shaked as I am the point of reference.

From a number point of view, this is hardly interesting. But from a graph’s point, it can be interesting. The first case is akin to drawing the 5 points star in a pentagon. The second case is akin to drawing the 5 points star in a pentagon twice. The last case is drawing and connecting the 5 points to a center point.

I think more clarifications is needed. For people arguing for common sense, please, the sense does not explain yellow is yellow.