## 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.