Answer: Identify the best strategy (algorithm) to help you think your way through the problem.

There is an infinite number of problems for us to solve but just a relatively small number of strategies needed to solve those problems. If we can learn those clever problem-solving strategies and know when to apply those strategies, we’ll be much better at solving problems.

Examples of clever strategies for solving various problems:

1.  What is the best strategy to use to solve this famous “Einstein puzzle”:

1. There are five houses.
2. The Englishman lives in the red house.
3. The Spaniard owns the dog.
4. Coffee is drunk in the green house.
5. The Ukrainian drinks tea.
6. The green house is immediately to the right of the ivory house.
7. The Old Gold smoker owns snails.
8. Kools are smoked in the yellow house.
9. Milk is drunk in the middle house.
10. The Norwegian lives in the first house.
11. The man who smokes Chesterfields lives in the house next to the man with the fox.
12. Kools are smoked in the house next to the house where the horse is kept. (should be “… a house …”, see Discussion section)
13. The Lucky Strike smoker drinks orange juice.
14. The Japanese smokes Parliaments.
15. The Norwegian lives next to the blue house.

Now, who drinks water? Who owns the zebra? In the interest of clarity, it must be added that each of the five houses is painted a different color, and their inhabitants are of different national extractions, own different pets, drink different beverages and smoke different brands of American cigarettes. One other thing: in statement 6, right means your right.— Life International, December 17, 1962

You can spend lots of frustrating hours or days thrashing your way through to a answer–or,more likely, you’ll get so tied up in knots you give up.

Or you can apply a simple organizational strategy that guides you to the answer in about ten minutes.

Click here for the clever strategy.

2.  What is the best strategy for solving this type of problem:

How would you prepare 500 mL of a 1:35 bleach solution from a 1:10 bleach solution using water?

You have come down with a bad case of the geebies, but fortunately your grandmother has a sure cure. She gives you an eyedropper bottle labeled:

Take 1 drop per 15 lb of body weight per dose four times a day until the geebies are gone. Contains gr 8 heebie bark per dr 100 solvent. 60 drops=1 tsp.

You weigh 128 lb, and the 4-oz bottle is half-full. You test the eyedropper and find there are actually 64 drops in a teaspoon. You are going on a three-week trip and are deeply concerned that you might run out of granny’s geebie tonic. Do you need to see her before leaving to get a refill?

(problems from Medication Math Problems)

This type of problem crops up often in daily living and is especially common for nurses. They are mathematically challenging, unless you know a strategy for solving them.

This is a  good strategy: apply dimensional analysis

A Guide to Dimensional Analysis