# Visualizing Problems

Standard

At first glance inductive reasoning appears as a hard concept, but it is not. I have learned that inductive reasoning is a simple vocabulary word that means forming a conclusion based on patterns, observations, examples, or experiments. Recognizing patterns is a very useful problem solving strategy. Observations, examples, and experiments are all great ways to help visualize patterns and form conclusions. An example of inductive reasoning is 2+2+4=8    4+5+7=16    8+12+4=24 all of the sums of the  problems are divisible by 4. This is an example of inductive reasoning because I used patterns and observations to solve the problem.

Counterexamples are another concept involved in problem solving. Counterexample is a very basic term used to describe an example that shows a statement to be false. An example of counterexample is that the opposite of a number is always positive. This is obviously false because the opposite of 2 is -2.

In many cases visualizing problems help to understand the problem.  Visualizing a problem can simply be writing out the answer in a chronological order. For example if a question asks how many 3 digit numbers can be written using 2, 5, and 8 only once. I start by writing all the ways that the 3 digit number can be written with 2 being the first number, then with 5 being the first number, and lastly 8 being the first number. Breaking down the problem helps to clearly see that there are 6 ways to write a 3 digit number using 2, 5, and 8 only once.

Example