Magical Well

Description


You are standing at a magical well. It has two positive integers written on it: a and b. Each time you cast a magic marble into the well, it gives you a \* b dollars and then both a and b increase by 1. You have n magic marbles. How much money will you make?

Example

For a = 1, b = 2, and n = 2, the output should be magicalWell(a, b, n) = 8.

You will cast your first marble and get $2, after which the numbers will become 2 and 3. When you cast your second marble, the well will give you $6. Overall, you’ll make \$8. So, the output is 8.

Input/Output

  • [execution time limit] 4 seconds (js)

  • [input] integer a

    Guaranteed constraints:
    1 \leq a \leq 2000.

  • [input] integer b

    Guaranteed constraints:
    1 \leq b \leq 2000.

  • [input] integer n

    The number of magic marbles in your possession, a non-negative integer.

    Guaranteed constraints:
    1 \leq n \leq 5.

  • [output] integer

[JavaScript (ES6)] Syntax Tips

1
2
3
4
5
6
// Prints help message to the console
// Returns a string
function helloWorld(name) {
console.log("This prints to the console when you Run Tests");
return "Hello, " + name;
}

Solution


1
2
3
4
5
function magicalWell(a, b, n) {
  return (
    a * b * n + ((a + b) * ((n - 1) * n)) / 2 + ((n - 1) * n * (2 * n - 1)) / 6
  );
}