--- Day 20: Infinite Elves and Infinite Houses ---
To keep the Elves busy, Santa has them deliver some presents by hand, door-to-door. He sends them down a street with infinite houses numbered sequentially: 1
, 2
, 3
, 4
, 5
, and so on.
Each Elf is assigned a number, too, and delivers presents to houses based on that number:
+-
+
- The first Elf (number
1
) delivers presents to every house:1
,2
,3
,4
,5
, ....
+ - The second Elf (number
2
) delivers presents to every second house:2
,4
,6
,8
,10
, ....
+ - Elf number
3
delivers presents to every third house:3
,6
,9
,12
,15
, ....
+
There are infinitely many Elves, numbered starting with 1
. Each Elf delivers presents equal to ten times his or her number at each house.
So, the first nine houses on the street end up like this:
+House 1 got 10 presents.
+House 2 got 30 presents.
+House 3 got 40 presents.
+House 4 got 70 presents.
+House 5 got 60 presents.
+House 6 got 120 presents.
+House 7 got 80 presents.
+House 8 got 150 presents.
+House 9 got 130 presents.
+
+The first house gets 10
presents: it is visited only by Elf 1
, which delivers 1 * 10 = 10
presents. The fourth house gets 70
presents, because it is visited by Elves 1
, 2
, and 4
, for a total of 10 + 20 + 40 = 70
presents.
What is the lowest house number of the house to get at least as many presents as the number in your puzzle input?
+