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1. The board has 5 spaces on it.

2. Your playing piece starts out on space number 1.

3. Each move consists of moving the piece to a randomly chosen space other than the one which you currently occupy (for example, if you are on space number 2, you randomly move to either space 1, 3, 4, or 5, with each space having equal chance of being selected, but you cannot stay on space number 2).

4. You win if, after seven moves, you are back on space 1.

The probability of winning this game is p. Find 4096p.

Suppose log.4a (40*sqrt(3)) = log.3a (45)

(Log.m (n) denotes log base m of n. sqrt(x) denotes the square root of x.)

Find a^3 (a^3 denotes "a cubed.")