Instructions

Test suite

Solution

Calculate the number of grains of wheat on a chessboard given that the number on each square doubles.

There once was a wise servant who saved the life of a prince. The king promised to pay whatever the servant could dream up. Knowing that the king loved chess, the servant told the king he would like to have grains of wheat. One grain on the first square of a chess board. Two grains on the next. Four on the third, and so on.

There are 64 squares on a chessboard.

Write code that shows:

- how many grains were on each square, and
- the total number of grains

Did you get the tests passing and the code clean? If you want to, these are some additional things you could try:

- Optimize for speed.
- Optimize for readability.

Then please share your thoughts in a comment on the submission. Did this experiment make the code better? Worse? Did you learn anything from it?

To run the tests, run the command `dotnet test`

from within the exercise directory.

Initially, only the first test will be enabled. This is to encourage you to solve the exercise one step at a time.
Once you get the first test passing, remove the `Skip`

property from the next test and work on getting that test passing.
Once none of the tests are skipped and they are all passing, you can submit your solution
using `exercism submit Grains.cs`

For more detailed information about the C# track, including how to get help if you're having trouble, please visit the exercism.io C# language page.

JavaRanch Cattle Drive, exercise 6 http://www.javaranch.com/grains.jsp

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
// This file was auto-generated based on version 1.2.0 of the canonical data.
using System;
using Xunit;
public class GrainsTest
{
[Fact]
public void Number_1()
{
Assert.Equal(1UL, Grains.Square(1));
}
[Fact(Skip = "Remove to run test")]
public void Number_2()
{
Assert.Equal(2UL, Grains.Square(2));
}
[Fact(Skip = "Remove to run test")]
public void Number_3()
{
Assert.Equal(4UL, Grains.Square(3));
}
[Fact(Skip = "Remove to run test")]
public void Number_4()
{
Assert.Equal(8UL, Grains.Square(4));
}
[Fact(Skip = "Remove to run test")]
public void Number_16()
{
Assert.Equal(32768UL, Grains.Square(16));
}
[Fact(Skip = "Remove to run test")]
public void Number_32()
{
Assert.Equal(2147483648UL, Grains.Square(32));
}
[Fact(Skip = "Remove to run test")]
public void Number_64()
{
Assert.Equal(9223372036854775808UL, Grains.Square(64));
}
[Fact(Skip = "Remove to run test")]
public void Square_0_raises_an_exception()
{
Assert.Throws<ArgumentOutOfRangeException>(() => Grains.Square(0));
}
[Fact(Skip = "Remove to run test")]
public void Negative_square_raises_an_exception()
{
Assert.Throws<ArgumentOutOfRangeException>(() => Grains.Square(-1));
}
[Fact(Skip = "Remove to run test")]
public void Square_greater_than_64_raises_an_exception()
{
Assert.Throws<ArgumentOutOfRangeException>(() => Grains.Square(65));
}
[Fact(Skip = "Remove to run test")]
public void Returns_the_total_number_of_grains_on_the_board()
{
Assert.Equal(18446744073709551615UL, Grains.Total());
}
}
```

```
using System;
public static class Grains
{
public static ulong Square(int n)
{
if (n < 1 || n > 64)
{
throw new ArgumentOutOfRangeException("n must be between 1 and 64");
}
return (ulong) Math.Pow(2, n - 1);
}
public static ulong Total()
{
return (ulong) Math.Pow(2, 64) - 1;
}
}
```

A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

## Community comments

The total number of grains is the sum of the powers of 2 from 0 to 63. The sum of the powers of two from 0 to n is two to the power of (n + 1) minus 1