This problem defines a sum.
1¹ + 2² + 3³ + 4⁴ + 5⁵ + 6⁶ + 7⁷ + 8⁸ + 9⁹ + 10¹⁰

Lets call that S10. We are told that S10 is equal to 10405071317.

Our task is now to find the last ten digits fo S1000.

This is relatively simple – I have solved similar problems before. The challenge is that

999^999

## [1] Inf

has an awfull lot of digits. The number is so large that R tells me it is infinite.

We are only interested in the last ten digits however, and R handles ten digits without problems.

Instead of using the built-in power function, I’ll make my own.

selfPower <- function(x){
  res <- 1
  for(i in 1:x){
    res <- (res*x)%%10000000000000
  }
  res
}

The function takes x as input. Multiply the result (initialized to 1) with x, and do that x times. After each multiplication, it keeps the last 13 digits as the result. Whatever happens with the rest of the digits is uninteresting.

I’ll run that function on all numbers from 1 to 1000. And then I’ll have to add it all together.
Adding stuff up, I’ll run into the same problem. So instead of using the built-in add-function, I’m writing my own.

adding <- function(x,y){
  (x+y)%%100000000000
}

It takes two numbers. Add them, and return the last 11 digits.

Putting that together, and doing a bit of functional programming using purrr:

library(purrr)
answer <- 1:1000 %>%
  (function(x) sapply(x, selfPower)) %>%
  reduce(adding) %>%
  (function(x) x%%10000000000)

I’m passing the numbers 1:1000 to an anonymous function, that sapply’s selfPower on the x’es. Then I reduce the results using adding. And finally that result is passed to a second anonymous function, that returns the last ten digits.

Lessons learned:
1. Anonymous functions should be inside parantheses.
2. I run a version of the magrittr library, that has an interesting error in the error message when you learn lesson 1: “Error: Anonymous functions myst be parenthesized”