尝试与犯错！

"Guess and check"

You've probably heard this many times. You may have thought, "Why should I bother guessing-and-checking when I know how to solve it more efficiently?" That's a perfectly legit thought. Go with your more efficient method.

Exactly. Trial and Error is a great way to start finding out how to do a problem when stuck. Try small cases, and check to see if they work. Maybe there's a pattern, but who knows? It's always best to follow your nose and experiment when stuck. And of course, if this happens to no avail (sometimes it will, and sometimes it won't), it's totally okay to ask for help. This time, you tried first, and maybe got somewhere.

If you do get something working, perhaps consider seeing if the same pattern extends for more cases. In some cases this may be the first steps to proving a pattern true by induction, one of the most powerful and widely used proof techniques in modern mathematics.

Here's a semi-math related puzzle!

Rules:

• Start on the tile $S$.
• You move either left, right, up, or down the number of spaces that are listed on the tile. Since you start on $S$ you will move $1$ tile.
• You cannot break up your movements into multiple directions. If you choose to move up you have to move that exact number up.
• You win when you reach tile $F$.

He moves 10 meters in a straight line to reach a point on a circle with a 10 meter radius an his starting point as the center. He then travels around the circle until he reaches a point at the edge of the forest - at most the circumference of the circle. His total distance is $(10\cdot2\pi) + 10$ meters or 72.83 meters to the nearest hundredth.

Trial and error is one of the most approved way of solving a problem with a bit or no knowledge. But perhaps for difficult answer, you cannot just try out the answer for infinity. Therefore one must always set a range and keep on eliminating the answers which you think is wrong. But always try to find a general formula as trial and error cannot give a clear way of solving that particular problem.