A Little Bite of Pi

It is well known by all math students that  is an irrational number. This means in simple English that its decimal form, troche which begins 3.141592…, goes on forever without any repeating blocks of digits.

To celebrate Pi Day this year – March 14, or 3/14 – we propose the following problem.

Beginning with the “decimal” digits (i.e. those that come after the initial 3), write the first 100 digits on a chessboard, one digit at a time in the squares, returning to the first square when necessary. See the diagram for how to begin.

chessboard

Now answer these questions:

  1. In which square of which row of the chessboard will the 100th digit be placed?
  2. What is that digit?
  3. What is the sum of the digits that are together in that square?

EXTRA: As this year is 2004, repeat items #1 and #2 for the case of the 2004th digit of .

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