Chapter 8, Problem 8.11PE

(Game: nine heads and tails) Nine coins are placed in a 3-by-3 matrix with some face up and some face down. You can represent the state of the coins using a 3-by-3 matrix with values 0 (heads) and 1 (tails). Here are some examples:

$\begin{array}{ccccc}\begin{array}{ccc}0& 0& 0\\ 0& 1& 0\\ 0& 0& 0\end{array}& \begin{array}{ccc}1& 0& 1\\ 0& 0& 1\\ 1& 0& 0\end{array}& \begin{array}{ccc}1& 1& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}& \begin{array}{ccc}1& 0& 1\\ 1& 1& 0\\ 1& 0& 0\end{array}& \begin{array}{ccc}1& 0& 0\\ 1& 1& 1\\ 1& 1& 0\end{array}\end{array}$

Each state can also be represented using a binary number. For example, the preceding matrices correspond to the numbers

000010000 101001100 110100001 101110100 100111110

There are a total of 512 possibilities, so you can use decimal numbers 0, 1, 2, 3, ... , and 511 to represent all states of the matrix. Write a program that prompts the user to enter a number between 0 and 511 and displays the corresponding matrix with the characters Hand T. Here is a sample run:

The user entered 7, which corresponds to 000000111. Since 0 stands for H and 1 for T, the output is correct.