"Slices" of Pi

Pi is a "normal number" - that is, the digits from 0-9 are distributed uniformly through its decimal expansion. Put differently, the digit 2 should appears roughly 10% of the time in the decimal expansion of Pi, or roughly 100,000 times in our 1,000,000 digit sample.

Following that logic:

1) the string "20" should appear about 1% of the 2-digit sequences, or 10,000 times in our 1,000,000 digit sample

2) the string "201" should appear about 0.1% of the 3-digit sequences, or 1,000 times in our 1,000,000 digit sample

3) the string "2017" should appear about 0.01% of the 4-digit sequences, or 100 times in our 1,000,000 digit sample

So, the answer should be closest to 100 . In fact, the string "2017" shows up exactly 101 times in the 1,000,000 digits of Pi.

Given that all digits are uniformly distributed in the decimal expansion of $\pi$ , any particular sequence of four digits should on average appear once out $10,000$ such sequences.

In $1,000,000$ , there are $1,000,000-3$ of these sequences, since they can start with any digit other than the last three.

The problem only looks for an approximate answer, so $\frac{999,997}{10,000}\approx100$ .