Every Possible Pick Three Lottery Number

There have been several times in my life when I have needed to print out every possible combination of some series. I once saw a contest in a "Games" magazine. They had a picture of a gumball machine with different colored gumballs and different letters on the gumballs. You were supposed to use 5 different colored gumballs and create real words from the 5 gumballs of the different colors. My sister-in-law and I wrote a computer program to print out all the possible combination of 5 letter words using the letters given and following the rule of 5 different color gumballs. The program would not be able to tell if what was printed was an actual word, but it would print every possible combination that fit the rules. Once the list was produced you would go down the list and check each one to see if it was a real word.

I posted the program at school, but I didn't want to run the program because it would use a lot of printer paper. One of my students did run the program and did get a very large printout. He did go through the list, but not as closely as he should have. He won second prize, but could have won the first prize. It turned out only a dozen people even entered and he did have all the answers. He only had to find the real words in the group. Even second prize was a brand new computer and $250.00.

I have had to print out every possible combination of a series of switches on a printer. As I experimented with different combinations I did not want to repeat ones I have already tried but also did not want to skip any that I should try. (Many older printers had such switches which were called "dip" switches. The big pain in this was that you had to completely power down the printer every time you changed the switches so that the printer would see the new setting on the "power up" sequence. If you change the switches while powered up nothing actually changes.

I got interested in how many possible pick three numbers were actually possible. Although I was aware there were a total possible of 1000 numbers, I did not fully appreciate the number of doubles or triples. I started to put this into a spreadsheet and started with:

000
001
002
003
004
005
006
007
008
009
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Now I had to figure out how to continue and simply moved the process to end up with:
010
011
012
013
014
015
016
017
018
109
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I am not going to list the entire series here for obvious reasons, but it did reveal that there were a lot more doubles and triples than I had originally thought and having such a list might help me better select numbers should I play the pick three especially if I were to check them as they were selected. Even though on a random basis they all have an equal chance of being selected at any given time over a very long run, they should all be picked in an equal frequency. There are some mathematicians that believe that random is not as random as we might think and that there is an order in chaos. If you whould want the entire list you could of course email me. My goal here is to consider how such lists of all events can lead to more understanding.

Recently I watched a program that showed researchers filming the wag of the tails of dogs as they looked at either their owner or a stranger. By observing many events like this they could show that the degree of wag is greater to one side for the owner. In any case listing all events can lead to discovery. By understanding all the ways that a word can be incorrectly spelled it helps us understand the range of problems with spelling people can have. Understanding all the instantaneous velocity values of a car as it accelerates gives us a better understanding of engine performance etc.