# The 100 Doors Puzzle in R at Rosetta Code

**Posted:**September 16, 2008

**Filed under:**programming, R-project, rosetta code 1 Comment

From time to time I see a puzzle at Rosetta Code that interests me, and I post an R solution for it. This time it was the 100 doors puzzle.

Problem: You have 100 doors in a row that are all initially closed. You make 100 passes by the doors. The first time through, you visit every door and toggle the door (if the door is closed, you open it; if it is open, you close it). The second time you only visit every 2nd door (door #2, #4, #6, …). The third time, every 3rd door (door #3, #6, #9, …), etc, until you only visit the 100th door.

Question: What state are the doors in after the last pass? Which are open, which are closed?

The code for this in R is pretty simple:

# UNOPTIMIZED

doors_puzzle <- function(ndoors=100,passes=100) {
doors <- rep(FALSE,ndoors)
for (ii in seq(1,passes)) {
mask <- seq(0,ndoors,ii)
doors[mask] <- !doors[mask]
}
return (which(doors == TRUE))
}
doors_puzzle()
## optimized version... we only have to to up to the square root of 100
seq(1,sqrt(100))**2
[/sourcecode]

What if you change the task to all the doors are initially opened, and we just send 10 persons (insted of 100), one after another, to change the state of the doore. First person change 5-10-15-20… and son on to 100. Next person change 10-20-30…-100, Third person 15-30-45….-90. Fourth person 20-40-…-100. And the last person (tenth person) change 50 and 100.