# 1546831721292591640116011560045710774439430123900352379195051

is the number of possible configurations of a

quiescent10-by-20

Tetris board. It's the evaluation of the

function (really,

expression: the function itself would have

20 as a

variable):

20
__ __
\ / \ **n**
\ | 10 |
1 + / | 2 - 2 |
__/ __ \ /
**n** = 1

The explanation for this: each possible Tetris row has one of 2^10 (1024) possible configurations, as each space may be in the state of a block "present" or "not present". There is one possible configuration which does not have any rows, the completely empty board, which accounts for the 1 in the equation.

The number of possible boards with exactly one non-empty row is 1022 (2^10 - 2), as no completely empty rows are allowed below any non-empty rows, and any full rows will be cleared. As for the number of boards with exactly two non-empty rows, it will be (2^10 - 2)^2, and so on from 1 through 20. Using sigma notation, the number is the summation which evaluates to the aforementioned huge number.