Project Euler: Problem 20

n! means n x (n - 1) x ... x 3 x 2 x 1

For example, 10! = 10 x 9 x ... x 3 x 2 x 1 = 3628800,
and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.
Find the sum of the digits in the number 100!

The approach to this problem is quite similar to problem 16 which we can see here. We just need to deal with a really large number here. So, GMP again to the rescue.

library(gmp)

x <- factorialZ(100)

sum(as.numeric(unlist(strsplit(as.character(x), split=""))))

# as.character(x) coverts the big number into a string

# strsplit() extracts individual elements of the string. This can be ensured by using the split = "" argument, which splits the string one element at a time

# strsplit() returns a list. To access the elements of this list, use unlist()

# convert the individual characters to numeric using as.numeric()

# sum the elements

Ans: 648

Project Euler: Problem 16

2¹⁵ = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.

What is the sum of the digits of the number 2¹⁰⁰⁰?

Handling large numbers or rather, very large numbers, can be a pain at times. But have no fear, for GMP is here.

GMP  makes the solution quite simple.

library(gmp)

x <- as.bigz(2^1000)

# as.bigz() is a function in the gmp library that helps dealing with large numbers quite easily 

This is the approach we take

1. Convert the number to a string so that we can extract the individual elements of the number
2. Extract the individual elements or digits
3. Create a vector of these digits
4. Sum the vector
5. Rejoice

sum(as.numeric(unlist(strsplit(as.character(x), split=""))))

# as.character(x) coverts the big number into a string

# strsplit() extracts individual elements of the string. This can be ensured by using the split = "" argument, which splits the string one element at a time

# strsplit() returns a list. To access the elements of this list, use unlist()

# convert the individual characters to numeric using as.numeric()

# sum the elements

Ans: 1366