3 ms·
It does seem like [n,n+1] is always unsolvable!
by jxding 2y ago
It does seem like [n,n+1] is always unsolvable!
- ahahahahah 2y ago[9,8] -> [6,3,8] -> [6,2,1,8] -> [6,2,9] -> [8,9]
- klyrs 2y agoIndeed, [n, n-1] [n-3, 3, n-1] [n-3, 2, 1, n-1] [n-3, 2, n] [n-1, n] Works for all n greater than... 6?
- klyrs 2y agoOptimizing self-response! That fails for six because n-3 and 3 co-occur. With a slight modification we can make it work for all n>5 [n, n-1] [2, n-2, n-1] [2, n-3, 1, n-1] [2, n-3, n] [n-1, n] edit: and it's not hard to show that n<6 are impossible, so the solution above is optimal in that sense.
- deleted 2y ago[deleted]
- adotbacon 2y agoYeah, the [n,n+1] is only a problem when there isn't enough wiggle room between the numbers. ex: [2,3] and [3,4] [3,4] --> [1,2,4] --> 4 can't split because 2/2 and 3/1 are invalid --> 4 can't initially split because 2/2 and 3/1 are both invalid [5,6] --> [5,4,2] --> [5,1,3,2] --> [6,3,2] --> [6,5] [7,8] --> [7,3,5] --> [7,1,2,5] --> [8,2,5] --> [8,7] When you add more numbers, you need more wiggle room. So, [4,5,6] is problematic and probably [5,6,7]. [4,5,6] --> [3,1,5,6] --> 6 can't break into 3, nor 5/1. It can do 4/2, but then 5 can't split. 5 also can't split. --> [4,2,3,6] --> [4,2,3,1,5] --> [6,4,5] --> 4 can't split into 2/2. It can split to 3/1 but then 5 can't split --> 6 can't initially split at all because 3/3, 4/2, and 5/1 are invalid Even if [6,7,8] has a solution, I'm sure [6,7,8,9] does not.
- madcaptenor 2y agoA solution for [6,7,8,9]: 6,7,8,9 6,3,4,8,9 6,3,4,8,2,7 9,4,8,2,7 9,4,8,2,1,6 9,4,3,5,2,1,6 9,7,5,2,1,6 9,7,5,3,6 9,7,8,6 9,5,2,8,6 9,5,2,1,7,6 9,5,3,7,6 9,8,7,6
- adotbacon 2y agoWow, well done! I found [6,7,8] as well: 6,7,8 6,7,5,3 6,7,1,4,3 6,8,4,3 6,8,7 6,3,5,7 6,2,1,5,7 8,1,5,7 8,6,7 8,4,2,1,6 8,4,3,6 8,7,6
- deleted 2y ago[deleted]