Max value

using System;

public static class Grains
{
    public static double Square(int i)
    {
        if (i is <= 0 or > 64)
            throw new ArgumentOutOfRangeException(nameof(i));

        return Math.Pow(2, i - 1);
    }

    public static double Total()
    {
        return UInt64.MaxValue;
    }
}

The maximum value for an unsigned integer gives the total number of grains on all sixty-four squares. It is essentially getting all of the bits of a 64-bit number set to 1.

This might seem like a "cheat". To understand how it works, consider just two squares that are represented in bits as 00.

• If there is a grain on square One, then the first bit (on the right) is set to binary 01, which is the decimal value of 1.
• If there are two grains on square Two, then the second bit (from the right) is set to binary 10, which is the decimal value of 2.
• If there are is one grain on Square One and two grains on square Two, then both bits are set to binary 11, which is the decimal value of 3.
• So, with all of the two bits set you get 3, which is the number of all grains on both squares.

Getting the value of System.UInt64.MaxValue is getting 64 bits set to 1, which is just what we need to get the total number of grains on sixty-four squares, given that the grains double on each square, starting with one grain on the first square.

Shortening

When the body of a function is a single expression, the function can be implemented as a expression-bodied member, like so

public static ulong Total() =>
  System.UInt64.MaxValue;

or

public static ulong Total() => System.UInt64.MaxValue;