problem solving
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How to start a problem solution

Starting a problem solution is the simplest (use Occam's razor), least time-consuming part of solving a problem. Starting a problem solution consists of applying the following two steps.

STEP 1: Identify what the problem asks for.

Ignore the details of the problem. Ignore the numbers and all the if's, and's and but's.
STEP 2. Respond to the request in the simplest manner possible.
Once what the problem asks for (the request) is identified, the response will be the answer to the question, "How would I find out?"

A problem solution is continued by using the two steps recursively. The solution steps will tell you when to use the if's, and's and but's. The numbers are used last.

Combining the responses generated provides the result (the answer to the problem).

The examples below provide you with exercise in starting a problem solution and continuing a problem solution.

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If Tom has three times as many apples as Susan and Susan has one-fourth as many as Joe, who has four, How many apples does Tom have?
There are six cubes. Half of the cubes are yellow. One cube is red. The rest of the cubes are blue. How many cubes are blue?
A man said to his son, "You are 10 years old and I am 3 times as old. The time will come when I will be only twice as old as you. How old will you be then?"
If Ann has $2.30 and Peggy has $1.90, how much must Ann give Peggy if Peggy is to have twice as much as Ann?
You need to travel to a neighboring city that is 230 miles away. You know that after 2 hours on the road you can increase your average speed by 10 miles per hour. What must be your average speed during the first two hours in order to make the trip in 5 hours?
A mixture problem
One solution has 10% chlorine and the other has 30% chlorine. How much of the 10% solution should be used to get 200 ml that is 17% chlorine?
The length of the banana.
A rope over the top of a fence has the same length on each side and weighs one-third of a pound per foot. On one end hangs a monkey holding a banana, and on the other end a weight equal to the weight of the monkey. The banana weighs two ounces per inch. The length of the rope in feet is the same as the age of the monkey, and the weight of the monkey in ounces is as much as the age of the monkey's mother.

The combined ages of the monkey and its mother are 30 years. One-half the weight of the monkey plus the weight of the banana is one fourth the sum of the weights of the rope and the weight.

The monkey's mother is one-half as old as the monkey will be when it is three times as old as its mother was when she was one half as old as the monkey will be when it is as old as its mother will be when she is four times as old as the monkey was when it was twice as old as its mother was when she was one-third as old as the monkey was when it was as old as its mother was when she was three times as old as the monkey was when it was one-fourth as old as it is now.

What is the length of the banana?


A complex problem is solved by successive solutions of simple problems. At each step Occam's razor provides an effective way of making decisions. Occam's razor can be simply stated using the acronym KISS (Keep It Simple Sweetheart)

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Copyright. Howard C. McAllister, 1997.