# Project Euler: Problem 16

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*2*

^{15}= 32768 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}?

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

- Convert the number to a string so that we can extract the individual elements of the number
- Extract the individual elements or digits
- Create a vector of these digits
- Sum the vector
- 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

To

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