Case Study: Determining Leap Year and Lottery

Leap Year

A year is a leap year if it is divisible by 4 but not by 100, or if it is divisible by 400.

You can use the following Boolean expressions to check whether a year is a leap year:

// A leap year is divisible by 4
boolean isLeapYear = (year % 4 == 0);
// A leap year is divisible by 4 but not by 100
isLeapYear = isLeapYear && (year % 100 != 0);
// A leap year is divisible by 4 but not by 100 or divisible by 400
isLeapYear = isLeapYear || (year % 400 == 0);

Or you can combine all these expressions into one like this:

isLeapYear = (year % 4 == 0 && year % 100 != 0) || (year % 400 == 0);

Lottery

The lottery program involves generating random numbers, comparing digits, and using Boolean operators.

Suppose you want to develop a program to play lottery. The program randomly generates a lottery of a two-digit number, prompts the user to enter a two-digit number, and determines whether the user wins according to the following rules:

1. If the user input matches the lottery number in the exact order, the award is $10,000.
2. If all digits in the user input match all digits in the lottery number, the award is $3,000.
3. If one digit in the user input matches a digit in the lottery number, the award is $1,000.

Note that the digits of a two-digit number may be 0. If a number is less than 10, we assume the number is preceded by a 0 to form a two-digit number. For example, number 8 is treated as 08 and number 0 is treated as 00 in the program.

package demo;
import java.util.Scanner;

public class Lottery {

    public static void main(String[] args) {
        // Generate a lottery number
        int lottery = (int)(Math.random() * 100);

        // Create a Scanner
        Scanner input = new Scanner(System.in);

        // Prompt user to enter a guess
        System.out.print("Enter your lottery pick (two digits): ");
        int guess = input.nextInt();

        // Get digits from lottery
        int lotteryDigit1 = lottery / 10;
        int lotteryDigit2 = lottery % 10;

        // Get digits from guess
        int guessDigit1 = guess / 10;
        int guessDigit2 = guess % 10;

        System.out.println("The lottery number is " + lottery);

        // Check the guess
        if(guess == lottery)
            System.out.println("Exact match: you win $10,000");
        else if(guessDigit2 == lotteryDigit1 && guessDigit1 == lotteryDigit2)
            System.out.println("Match all digits: you win $3,000");
        else if(guessDigit1 == lotteryDigit1 || guessDigit1 == lotteryDigit2 || guessDigit2 == lotteryDigit1 || guessDigit2 == lotteryDigit2)
            System.out.println("Match one digit: you win $1,000");
        else
            System.out.println("Sorry, no match");
    }

}

Note that guess % 10 obtains the last digit from guess and guess / 10 obtains the first digit from guess, since guess is a two-digit number.