The Handshake Math Problem [Reasoning]

The Handshake math problem is a common question encountered in selective reasoning tests. This problem typically revolves around a scenario where a group of people shake hands with each other, and the test taker is required to determine the total number of handshakes that occur. The Handshake problem is designed to assess an individual's ability to apply logical reasoning and mathematical thinking to solve complex problems. By analyzing the relationships and patterns within the given scenario, test takers are challenged to employ deductive reasoning and mathematical formulas to arrive at the correct solution. The Handshake math problem serves as an excellent measure of one's analytical skills, critical thinking, and problem-solving abilities in a time-constrained setting.

Question 1: If there are 2 people in a room and every person shakes hands exactly once with all of the other people, how many handshakes will there be? 

with a small group this question is easy to answer. Since there are only 2 individuals and they both shake hands with each other that makes only 1 hand shake. 

However what if the number of people are increased to a very large group how would you solve this question easily. 

This is easy by using the formula below. This is because each of the n people can shake hands with (n-1) people (they would not shake their own hand), and the handshake between two people is not counted twice as stated in the question.

This formula can be used for any number of people. For example, with a party of 98 people, find the number of handshakes possible.

Question 2:  If there are 98 people in a room and every person shakes hands exactly once with all of the other people, how many handshakes will there be? 

So, there are 4753 handshakes that can be made between 98 people.

The same formula can be used for similar pattern question in a different context. For example,

If there are 20 football teams in a tournament how many games must be played in order for each team to play every other team exactly once?

*Important to note (exactly once) 

Answer: Number of games played (T) = n(n-1)/2

T = 20(20-1)/2

   = 20 x 19/2 = 190 Games