Use the methods in the following program to print 100 uppercase letters and then 100 single digits, printing ten per line.

1   public class RandomCharacter {
2       /** Generate a random character between ch1 and ch2 */
3       public static char getRandomCharacter(char ch1, char ch2) {
4           return (char)(ch1 + Math.random() * (ch2 - ch1 + 1));
5       }
6
7       /** Generate a random lowercase letter */
8       public static char getRandomLowerCaseLetter() {
9           return getRandomCharacter('a', 'z');
10      }
11
12      /** Generate a random uppercase letter */
13      public static char getRandomUpperCaseLetter() {
14          return getRandomCharacter('A', 'Z');
15      }
16
17      /** Generate a random digit character */
18      public static char getRandomDigitCharacter() {
19          return getRandomCharacter('0', '9');
20      }
21
22      /** Generate a random character */
23      public static char getRandomCharacter() {
24          return getRandomCharacter('\u0000', '\uFFFF');
25      }
26  }

The area of a pentagon can be computed using the following formula:

$$\text { Area }=\frac{5 \times s^2}{4 \times \tan \left(\frac{\pi}{5}\right)}$$

Write a method that returns the area of a pentagon using the following header:

public static double area(double side)

Write a main method that prompts the user to enter the side of a pentagon and displays its area.

(Print calendar) Programming Exercise 3.21 uses Zeller’s congruence to calculate the day of the week. Simplify Listing 6.12, PrintCalendar.java, using Zeller’s algorithm to get the start day of the month.

(Current date and time) Invoking System.currentTimeMillis() returns the elapsed time in milliseconds since midnight of January 1, 1970. Write a program that displays the date and time. Here is a sample run:

Current date and time is May 16, 2012 10:34:23

Craps is a popular dice game played in casinos. Write a program to play a variation of the game, as follows:
Roll two dice. Each die has six faces representing values 1, 2, ..., and 6, respectively. Check the sum of the two dice. If the sum is 2, 3, or 12 (called craps), you lose; if the sum is 7 or 11 (called natural), you win; if the sum is another value (i.e., 4, 5, 6, 8, 9, or 10), a point is established. Continue to roll the dice until either a 7 or the same point value is rolled. If 7 is rolled, you lose. Otherwise, you win.

Your program acts as a single player. Then, revise the program run it 10,000 times and display the number of winning games.

Credit card numbers follow certain patterns. A credit card number must have between 13 and 16 digits. It must start with

• 4 for Visa cards
• 5 for Master cards
• 37 for American Express cards
• 6 for Discover cards

In 1954, Hans Luhn of IBM proposed an algorithm for validating credit card numbers. The algorithm is useful to determine whether a card number is entered correctly, or whether a credit card is scanned correctly by a scanner. Credit card numbers are generated following this validity check, commonly known as the Luhn check or the Mod 10 check, which can be described as follows (for illustration, consider the card number 4388576018402626):

• Double every second digit from right to left. If doubling of a digit results in a two-digit number, add up the two digits to get a single-digit number.

(Game: craps) Craps is a popular dice game played in casinos. Write a program to play a variation of the game, as follows: Roll two dice. Each die has six faces representing values 1, 2, . . ., and 6, respectively. Check the sum of the two dice. If the sum is 2, 3, or 12 (called craps), you lose; if the sum is 7 or 11 (called natural), you win; if the sum is another value (i.e., 4, 5, 6, 8, 9, or 10), a point is established. Continue to roll the dice until either a 7 or the same point value is rolled. If 7 is rolled, you lose. Otherwise, you win. Your program acts as a single player. Here are some sample runs.

You rolled 5 + 6 = 11
You win

You rolled 1 + 2 = 3
You lose

You rolled 4 + 4 = 8
point is 8
You rolled 6 + 2 = 8
You win

You rolled 3 + 2 = 5
point is 5
You rolled 2 + 5 = 7
You lose

(Palindrome integer) Write the methods with the following headers:

// Return the reversal of an integer, e.g., reverse(456) returns 654
public static int reverse(int number)

// Return true if number is a palindrome
public static boolean isPalindrome(int number)

Use the reverse method to implement isPalindrome . A number is a palin- drome if its reversal is the same as itself. Write a test program that prompts the user to enter an integer and reports whether the integer is a palindrome.

How do you simplify the max method in Listing 6.1 using the conditional operator?

Twin primes are a pair of prime numbers that differ by 2. For example, 3 and 5 are twin primes, 5 and 7 are twin primes, and 11 and 13 are twin primes. Write a program to find all twin primes less than 1,000. Display the output as follows:

(3, 5)
(5, 7)
...

A prime number is called a Mersenne prime if it can be written in the form 2 p - 1 for some positive integer p. Write a program that finds all Mersenne primes with p 31 and displays the output as follows.

p                 2^p-1
----------------------
2                 3
3                 7
5                 31
...

(Emirp) An emirp (prime spelled backward) is a nonpalindromic prime number whose reversal is also a prime. For example, 17 is a prime and 71 is a prime, so 17 and 71 are emirps. Write a program that displays the first 120 emirps. Display 10 numbers per line, separated by exactly one space, as follows:

13 17 31 37 71 73 79 97 107 113 149 157 167 179 199 311 337 347 359 389 ...

A palindromic prime is a prime number and also palindromic. For example, 131 is a prime and also a palindromic prime, as are 313 and 757. Write a program that displays the first 100 palindromic prime numbers. Display 10 numbers per line, separated by exactly one space, as follows:

2 3 5 7 11 101 131 151 181 191
313 353 373 383 727 757 787 797 919 929
...

Write a method that converts milliseconds to hours, minutes, and seconds using the following header:

public static String convertMillis(long millis)

The method returns a string as hours:minutes:seconds. For example, convertMillis(5500) returns a string 0:0:5, convertMillis(100000) returns a string 0:1:40, and convertMillis(555550000) returns a string 154:19:10.