Okay, so today I was messing around with numbers and got curious about how many different numbers I could make using just the digits 1, 2, 0, and 1. It seemed like a fun little puzzle, so I grabbed a pen and paper and started figuring it out.
The First Attempts
First, I tried to arrange them to make 4-digit numbers. You know, starting with the biggest possible number and working my way down. I quickly realized the zero couldn’t be in the first spot, ’cause that would make it a 3-digit number. So, I started with 2, then 1, 1, and 0 – that gave me 2110. Then I switched things around a bit and got 2101, 2011, 1210, 1201, 1120, 1102, 1021, and 1012. Phew! Seems like a lot already.
Getting Systematic
But then I thought, “Wait a minute, what about 3-digit numbers? Or 2-digit? Or even just single-digit ones?” I decided I needed to be more systematic, or I’d probably miss some.
- 3-digit numbers: I figured I could use the same logic, just ignoring one of the digits each time. I made sure to account for the zero not being at the beginning.
- 2-digit numbers: This got a little easier. I just paired up the digits, again, making sure zero wasn’t in the leading position.
- 1-digit numbers: This was the easiest! Just 0,1,2.
Counting It All Up
After listing them, I Counted it, there were 9 four-digit numbers I found earlier.
Then, there is a good chunk of 3-digit numbers. And a few 2-digit numbers. Finally, the easy 1-digit numbers 0, 1 and 2.
I double-checked everything, made sure I didn’t repeat any, and finally had my answer. It took a bit of scribbling and thinking, but it was a neat way to spend a bit of time! I made the numbers, I listed them, and I am pretty satisfied now.
