Hints for the Patterns in Pascal’s Triangle Problem

In what rows are all of the values odd? What is the pattern in the number of odds for the rows up to and including these all-odd rows?

If you are having trouble generating the values for the entries in the longer rows of the triangle, is there a way for you to keep track of their oddness or evenness (or their remainder when divided by some other value) without keeping track of the values themselves?

A fractal is a self-similar geometric figure. That is, under a certain scaling (enlargement or reduction), it looks like itself. In what way is a version of Pascal’s triangle, colored according to the parity of its entries, fractal-like? What would the scaling factor be?

For many reasons, the initial row of Pascal’s triangle with just one “1” is called row number 0, the next row, with two 1’s, is row number 1, etc. Try using this numbering scheme in your analyses.