# Euler Problem 16: Power Digit Sum

Euler Problem 16 is reminiscent of the famous fable of wheat and chess. Lahur Sessa invented the game of chess for King Iadava. The king was very pleased with the game and asked Lahur to name his reward.

Lahur asked the king to place one grain of rice on the first square of a chessboard, two on the next square, four on the third square and so on until the board is filled. The king was happy with his humble request until his mathematicians worked out that it would take millions of tonnes of grain. Assuming there are 25 grains of wheat in a gramme, the last field will contain more than 461,168,602,000 tonnes of grain.

## Euler Problem 16 Definition

$2^{15} = 32768$ and the sum of its digits is $3 + 2 + 7 + 6 + 8 = 26$. What is the sum of the digits of the number $2^{1000}$?

## Solution

The most straightforward solution uses the GMP package for Multiple Precision Arithmetic to calculate big integers. The as.bigz function results in a special class of arbitrarily large integer numbers

library(gmp)
digits <- as.bigz(2^1000) # Define number

$2^4 = 2 \times 2 \times 2 \times 2 = ((2+2)+(2+2)) + ((2+2)+(2+2))$
pow <- 2