Lesson 1: Strategy

The first in a nine part series originally written and published by ePeterso2as part of his Puzzle Solving 101 Series. Reprinted here with permission of the author.

"Where the heck do you start?"

That's probably the best question I've ever been asked when it comes to puzzle solving. When I set out to tackle a puzzle, here's the general strategy I use to try to pick it apart.

1. Begin with the End in Mind

This is one of Stephen Covey's Seven Habits of Highly Effective People. It simply means that you should try to visualize what your result will be before you start looking for it.

For example, suppose I told you to go find a regular-size traditional cache at a particular set of coordinates. You would already have an idea of how big that would be and would focus your efforts on things at those coordinates that could be about that size. You would approach the same set of coordinates very differently if I told you it was a nano tube instead of an ammo box.

Puzzle caches are the same way - the descriptions typically give you hints as to what their solutions will look like. The solution to a puzzle is typically (but not always) a set of coordinates, so keep an eye out for ways in which coordinates might be represented.

In our area, both the north and west coordinates are usually expressed in seven digits each. So, a pair of seven things in a puzzle description is a strong hint that those things will ultimately become the coordinates in your solution. A pair of five things might be the coordinates of the minutes, using along with the degrees of the posted coordinates. A pair of three things might be the fraction of minutes in each coordinate.

2. Take Stock of What You Know

Make a list of the basic facts as presented to you. Don't let your own biases or preconceptions limit or polarize your thinking. Just get a quick inventory of what you're given and keep it separate from what you think you know about what you're given. For example, consider this little brain teaser:

Plant ten trees so that the trees are in five rows of four trees each.

Five rows of four trees seems to imply that twenty trees are needed, so it's clearly not possible to do it with ten. But no constraints on how those trees can be arranged are given ... in fact, there are at least six different ways to do it.

Puzzle writers often exploit the differences between what you know and what you assume. It's always best to avoid jumping to conclusions unless you are totally sure of the facts on which those conclusions are based.

3. Look for Patterns

Many puzzles involve recognizing and using patterns of information. Being able to spot those patterns is often the key to solving the puzzle. For instance, suppose you were given the following information:

Green-0 Yellow-1 Red-2 Violet-4 Blue-4 Orange-6 Indigo-7

You might notice that those are the basic colors of the rainbow - the rainbow is the pattern. Arrange the numbers in rainbow order and you get "2610474", which could be "N 26 10.474" (half of a pair of coordinates).

Any time you see some common thread among the information bits that you're given, that might be significant. Information can be ordered (such as the colors of a rainbow) or unordered (like a league of professional sports teams).

Just because the bits of information you've got can be grouped or interpreted in a logical way doesn't mean that it's relevant to the puzzle. There's no real general-purpose way to tell what's relevant and what isn't - good puzzle writers like to keep you guessing about those sorts of things. Figuring out what's important and what isn't is often a matter of trial and error.

4. Make Educated Guesses

Sometimes you've drawn all of the conclusions you can from the facts of your puzzle but you still don't have it solved. Now what? This is where educated guessing comes in.

You may know educated guessing by its more formal name: the Scientific Method. You make a guess, then you do some tests to see if that guess is true or false. If it's true, then you add that guess to your knowledge base. If it's false, you scrap it, go back to the point where you guessed, and guess again.

Consider solving a maze. You know where the start and the end are, but you have no idea which path is the proper one. So you start at the beginning and work your way through it until you come to a fork. Now you've got two or three different paths you can take ... but which one's the right one? The only way to find out is to pick one and carry on. If you come to a dead end, then go back to that fork in the road and go the other way.

But suppose you've made your guess as to what the right path is and you come to another fork in the road. Now you've got to guess again. Keep track of your guesses so that you can "unwind" in case your the guesses based upon your guesses turn out to be wrong.

If you're a video gamer, marking the place where you've made a guess is like reaching a save point - if you mess up later in the game, you can always return to your last save point.

5. Find the Light Switch

In 1995, Andrew Wiles proved one of the most famous conjectures in all of mathematics, Fermat's Last Theorem. His proof, which he constructed in secrecy over seven years, was long and complex. He described his work in proving the theorem this way:

Imagine that you are in a large, unfamiliar mansion at night and all of the lights are off. You slowly feel your way around the room, discovering what objects are there by touch, slowly learning where they are in relation to one another. Eventually, you find your way to the wall and locate the light switch and turn it on. All of the sudden, you can clearly see everything. Then you move on to the next dark room and start over again, repeating the process until the whole mansion is illuminated.

Some puzzles are like large mansions with many rooms, while other puzzles may be more like a one-room apartment. These rooms may come in different sizes with different numbers of objects in them. But typically there is one small key - one "light switch" - that illuminates each room. To solve the puzzle, your mission is to find that key.

For instance, you may not know what to make of this:

0x1A 0xC 0x159 / 0x50 0x36 0x141

But when you discover that "0x" means that the numbers are hexadecimal (base 16) instead of base 10, then decoding them to "26 12 345 / 80 54 321", or "N 26 12.345 W 80 54.321", becomes trivial.

Resources you can use to discover things like that will be covered in the next lesson.

Think you paid attention in class? Try Exercise 1 found at GCYXZ1 Puzzle Solving 101 - Lesson 1: Strategy.

Save your answer...it will be important later...