Have a look at these two sequences.
120
222
333
444
555
675
777
897
9117
10119
111210
121410
131610
141612
151614
161814
172014
182115
192216
202317
212319
222321
232323
242523
* * *
120
240
360
471
582
6102
7122
8133
9144
10164
11175
12195
13215
14226
15237
16257
* * *
Now, have a look at these wrong sequences, which are malformed according to the rules underlying the sequence.
120
222
333
444
555
675
777
897
9117
10119
111210
111311
121511
131711
141812
151814
162014
172016
182117
192218
202319
212321
222521
232523
242624
* * *
120
222
333
444
555
675
777
897
9117
10119
111210
121410
131610
141612
151614
161814
172014
182115
192216
202317
212319
222321
232424
242624
* * *
A LLM could not solve this problem on its own, requiring many hints before it finally stumbled across the correct answer. Can you do better?
Here are some hints for you, fair reader. If you can complete it without using all of them, you have done better than the bot. If you can complete it without using any, you’re either a puzzle solving mastermind or very in tune with how I think. Each hint is broken up by a line, like so: ^ ^ ^
^ ^ ^ ^ ^ ^ ^
Hint #1: It’s not a traditional mathematical number sequence – that is, the number as a whole doesn’t progress by a single rule which is consistently applied from one number to the next. It consists of multiple variables, two of which are affected by a single external (undescribed, but predictable when you understand the incrementation) condition.
^ ^ ^ ^ ^ ^ ^
Hint #2: The sequence terminates because of an external condition.
^ ^ ^ ^ ^ ^ ^
Hint #3: The chief external condition that controls the middle and end values, from a mathematical point of view, a variable with three possible states. It can vary from row to row.
^ ^ ^ ^ ^ ^ ^