learn-z3

Some simple example challenges to get started with z3.

Simple Equation

Solve for x & y where x + 2y = 7, x > 2 and y < 10

Solution

Logical Reasoning

John, Aries, and Joseph are brothers with different ages.

1. Aries is the oldest.
2. John is not the youngest.

Who is the youngest brother?

Solution

Calculate Distribution

Spend exactly 100 dollars and buy exactly 100 animals.

• Dogs cost 15 dollars
• Cats cost 1 dollar
• Mice cost 25 cents each.

You have to buy at least one of each. How many of each should you buy?

Solution

Match Assignment

There is an assignment of unique digits to letters such that the equation send + more = money holds. Find an assignment of the digits to make this true.

Solution

Magic Square

A square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.

Magic square of 15 looks like:

8 1 6
3 5 7
4 9 2

Generate a magic square of 15 with z3.

Solution

Simple Weak Hash

Following is a simple hash, find the string s such that it satifies the statement n == n2.

private static boolean hash(final String s) {
    int n = 7;
    final int n2 = 593779930;
    for(int i = 0; i < 6; ++i) {
        n = n * 31 + s.charAt(i);
    }
    return n == n2;
}

Solution

Sudoku

Solve the following sudoku with z3.

0 0 0 0 9 4 0 3 0
0 0 0 5 1 0 0 0 7
0 8 9 0 0 0 0 4 0
0 0 0 0 0 0 2 0 8
0 6 0 2 0 1 0 5 0
1 0 2 0 0 0 0 0 0
0 7 0 0 0 0 5 2 0
9 0 0 0 6 5 0 0 0
0 4 0 9 7 0 0 0 0

Solution