Project Euler: Problem 16

$2^{15} = 32\,768$ and the sum of its digits is $3 + 2 + 7 + 6 + 8 = 26$

What is the sum of the digits of the number $2^{1000}$

– Project Euler Problem 16

Solution

With the big integer type IntX (which I added to my project to solve an earlier problem) this one is pretty much as easy as you'd think.

var answer = IntX
    .Pow(2, 1000)
    .ToString()
    .Select(x => x - '0')
    .Sum();

It first does the calculation and then gets the string representation of the result. And in case you were wondering, that would be:

10715086071862673209484250490600018105614048117
05533607443750388370351051124936122493198378815
69585812759467291755314682518714528569231404359
84577574698574803934567774824230985421074605062
37114187795418215304647498358194126739876755916
55439460770629145711964776865421676604298316526
24386837205668069376

And as a comparison, here is the largest number that can be represented using built-in .Net types. decimal.MaxValue.

79228162514264337593543950335

As you can see, the first number is kind of bigger than the second 😛 Aaaanyways, the next bit might be a bit cryptic. But fear not, it is actually quite simple:

• A string is an array of characters.
• All characters have a character code (a numeric value).
• The character codes for the numeric characters ('0', '1', and so on) comes after each other, which means that for example '1' has a character code value which is 1 larger than the character code of '0'.
• If we take a character code and subtracts it from itself, we get zero. (Thank you captain obvious...)
• This means that if we subtract '0' from '0', we get 0. And if we subtract '0' from '5', we get 5. (Oh, right, clever!)

So, the last two lines in my code simply converts all the characters in the string into actual numbers and then sums them together. Which would get us the answer! Tadaa 🤯

How did you do? Have you found a more interesting solution? Please do share. 🙂