Bit-shifting

export function square(num) {
  if (num < 1 || num > 64) {
    throw new Error('square must be between 1 and 64');
  }
  return 1n << (BigInt(num) - 1n);
}

export function total() {
  return (1n << 64n) - 1n;
}

Instead of using math to calculate the number of grains on a square, you can set a bit in the correct position of a BigInt value.

To understand how this works, consider just two squares that are represented in binary bits as 00.

You use the left-shift operator to set 1n at the position needed to make the correct decimal value.

• To set the one grain on Square One you shift 1n for 0 positions to the left. So, if num is 1 for square One, you subtract num by 1 to get 0, which will not move it any positions to the left. The result is binary 01, which is decimal 1.
• To set the two grains on Square Two you shift 1n for 1 position to the left. So, if num is 2 for square Two, you subtract num by 1 to get 1, which will move it 1 position to the left. The result is binary 10, which is decimal 2.

For total we want all of the 64 bits set to 1 to get the sum of grains on all sixty-four squares. The easy way to do this is to set the 65th bit to 1 and then subtract 1. To go back to our two-square example, if we can grow to three squares, then we can shift 1n two positions to the left for binary 100, which is decimal 4. By subtracting 1 we get 3, which is the total amount of grains on the two squares.

Shortening

When the body of a function is a single expression, the function can be implemented as an arrow function, like so

export const total = () => (1n << 64n) - 1n;