If you remember the day in class that we played the guessing game, it really helped Chris to figure out the rule when we grouped all of the liars together. Then he could see the fact that people were wearing stripes. So, organizing your data is important when you are trying to draw an inference.

In the table below, I have provided one possible way to organize your data for converting "terminators" into decimals. I did the first few for you, so you could see what you need to do to fill in the chart. Then I gave you a few examples to try. For the blank rows, you make up the example and fill in the chart. Then you just need to stare at the various columns until you have a method that will always work. Once you get it, you should be able to fill in the columns for 27519, without ever using a calculator.

After that, try to make a generalization for 2a5b. The rule may need a few "ifs" but try to express it as simply as possible. Once you have a rule that is guaranteed to work for any value of a (>=0), any value of b (>=0), then you have your proof!