Why I Write Problems

1. There are super difficult problems out there.

It all started with a problem in logic that I considered to be super difficult. I was startled when I read the solution. How could I have possibly conceived such a strategy? How do I progress into that? Well, solving a bunch of super hard problems seems like a very difficult and unreliable way to do it. After all, isn't my problem for solving super hard problems is that they're are super hard? I could eventually get used to that and start seeing something. There might be another less stressful way however. Those problems were conceived and hence the strategy is the result of it's conception. Then why shouldn't I try that?

1. It helps me understand things better.

If you have solve some of my problems, you will notice that they are generally not that difficult. This is because most of them have been inspired by me trying to understand something rather than trying to challenge others. Of course, I do want to eventually want to challenge others (I've written two difficult ones), but for now, my focus is my own understanding. I just had this experience. For some reason, I couldn't grasp the idea of a mechanical adder, or mechanical binary adder. Things that I thought were the case were not the case. So I wrote a problem by looking for an analogy:

Binary Sequencing Suppose that Marla, John and Bob want to play poker. Bob decided that if both Marla and John play a round, then he would simply watch and then he will play the next one. Each player will take a break for the next round after having played one. If only Marla or only John plays, then Bob will sit back until both had played. The tournament lasted 4 rounds and both Marla and John played the first one. How many rounds did Bob played?

The problem itself its not hard but here's what's going on. We can represent a player taking a round with a 1 and a player taking a break with a 0. Bob plays only if the two others have played, this is the equivalent of "carrying" a 1. In particular, since Marla and John both player the first round, then we have 1+1 = 10 in binary. I added details so that the problem makes sense, that is, what are the other digits? Since Marla and John played the first round, then they will take a break the second round thus the next digits are 0+0 plus the 1 because Bob now plays (the carrying of 1). The "sequencing" needs to stop, so I included up to 4 rounds in the story. The result is the same as adding 101+101=1010. After this, I got a grasp of what a mechanical adder is.

1. There's a lot to learn by taking your time with concepts.

What I was doing wrong is that I just wanted to solve, solve, and solve. This could mean that as long as I got a problem, there was no reason to stick around. Writing problems using a newly, or already acquired concept kind of give me more appreciation for what I'm doing. This new motivation transfers into knowledge. In my Binary Sequencing problem, even if I had understood what a mechanical adder is, I might have not known that this idea is not restricted to logic gates. I wrote a similar problem for base 4/3 using ice-cubes. Again, the problems themselves are easy but there's more to just solving. I feel like there's a reason behind solving other than just becoming better at solving.

1. It helps with building appropriate analogies

So I numbering these reasons in base 4 starting with 1. We could say that 4=0 in the sense that the 4th reason is labeled 0. In fact, an appropriate analogy for adding 101+101 base 2 would be the setting given in the problem. I think analogies a very important. It's a part of communicating and understanding.