There is no such thing as magic. We will have fun with this game and at the end we will have the responsibility to take anything of value and match it up to something that is real.
Simple Integers
We should expect simple integers to occur in math and science. We know experimental error exists and when we see 1.997 we tend to believe the correct amswet is probably 2. This kind of thinking helped scientists decide there were two atoms of hydrogen for every one atom of oxygen in a molecule of water.
Likes Come From Likes
It is not a guarantee, but we can ecpect something to produce something like itself. For example, if we take the derivative of a trigonometric function, it makes sense the results should be another trigonometric function, or something built using trigonometric functions.
Interchangability
If the formula has two variables that we know to be interchangeable, then this puts limits on what is possible for the answer, and that may be enough to guide us to the final answer.
Theory of Limits
Vectoreverything 