Numbers of Ways

It’s time for a thought experiment. You’ve got boxes, and you’ve got toys.

If you have 3 boxes and you can fit one toy in each box, there are 4 possible ways to fill the boxes with toys: all 3 filled, 2 filled, 1 filled, or 0 filled.

So you can fill a number of boxes in one more than the number ways.

Following this pattern, if you have 0 boxes, then you can still have 0 boxes filled; there is still 1 way to fill your number of boxes with any number of toys.

Yes, this is an equivalency; having transcended the idea of having boxes, we are now imagining the extreme. And so, purely depending on which perspective we take, we either have no ways to fill boxes, one way (as I stated), or infinite ways (you can fill a nonexistent box in any manner you like, because it won’t really happen – you can transcend the rules of one toy per box and input any count of toys into the box!). Or we can see how this was just a game being played in the first place, and boxes really don’t have rules for a number of toys fitting inside, and boxes can fall apart, and toys can come in different sizes, and so on and so forth. There is always an exception to a rule, so rules are really contrivances, not universal truths. What’s the value in realizing this? Counting the number of ways something can be done is just a contrivance… so don’t let that limit you! Realize there is always another way of considering doing something. Maybe you failed to get something done one day. Instead, transcend the issue and realize how you did or learned something else!