I tried the same prompt a lot of times and saw "chain of thought" attempts complete with the state modeling... they must be augmenting the training dataset with some sort of script generated crap.

I have to say those are so far the absolute worst attempts.

Day 16 (Egg 3 on side A; Duck 1, Duck 2, Egg 1, Egg 2 on side B): Janet takes Egg 3 across the river.

"Now, all 2 ducks and 3 eggs are safely transported across the river in 16 trips."

I kind of feel that this undermines the whole point of using transformer architecture instead of a recurrent neural network. Machine learning sucks at recurrence.

Well I'll be damned, they are trying to get it to work as if it had internal state, by augmenting their training dataset with some auto-generated crap. Of course, if machine learning wasn't shit at recurrence they wouldn't be using transformer architecture, so it doesn't work.

I got the following from chatgpt:

Janet’s ducks lay 3 eggs per day. Each day, she transports one duck and all the eggs to the other side of the river using a boat that can hold her and one other item (either a duck or an egg). How does she do that? ChatGPT

Janet can transport the ducks and eggs across the river using the following strategy:

Day 1 (Duck A, Duck B, Duck C on side A; Egg 1, Egg 2, Egg 3 on side A):
    Janet takes Duck A across the river.

Day 2 (Duck B, Duck C on side A; Egg 1, Egg 2, Egg 3 on side A):
    Janet takes Egg 1 across the river.

Day 3 (Duck B, Duck C on side A; Egg 2, Egg 3 on side A; Duck A on side B):
    Janet takes Duck A back to side A.

Day 4 (Duck C on side A; Egg 2, Egg 3 on side A; Duck A on side A; Egg 1 on side B):
    Janet takes Duck B across the river.

Day 5 (Duck C on side A; Egg 2, Egg 3 on side A; Duck A on side A; Egg 1, Duck B on side B):
    Janet takes Egg 1 back to side A.

Day 6 (Duck C on side A; Egg 2, Egg 3 on side A; Duck A, Egg 1 on side A; Duck B on side B):
    Janet takes Duck A across the river again.

Day 7 (Egg 2, Egg 3 on side A; Duck A, Egg 1 on side A; Duck B on side B; Duck C on side A):
    Janet takes Duck C across the river.

Day 8 (Egg 2, Egg 3 on side A; Duck A, Egg 1, Duck C on side A; Duck B on side B):
    Janet takes Egg 2 across the river.

Day 9 (Egg 3 on side A; Duck A, Egg 1, Duck C on side A; Duck B on side B; Egg 2 on side B):
    Janet takes Duck A back to side A.

Day 10 (Egg 3 on side A; Duck C on side A; Duck A on side A; Duck B, Egg 1, Egg 2 on side B):
    Janet takes Duck B across the river.

Day 11 (Egg 3 on side A; Duck C on side A; Duck A, Duck B on side A; Egg 1, Egg 2 on side B):
    Janet takes Egg 1 back to side A.

Day 12 (Egg 3 on side A; Duck C on side A; Duck A, Egg 1, Duck B on side A; Egg 2 on side B):
    Janet takes Duck A across the river again.

Day 13 (Duck C on side A; Duck A, Egg 1, Duck B on side A; Egg 2 on side B; Egg 3 on side B):
    Janet takes Duck C across the river.

By following this sequence, Janet successfully transports all 3 ducks and all 3 eggs across the river in 13 trips. Each trip involves either transporting one duck or one egg, adhering to the constraint that Janet can only carry one item (duck or egg) with her in the boat.

Well the problem is it not having any reasoning period.

Not clear what symbolic reasoning would entail, but puzzles generally require you to think through several approaches to solve them, too. That requires a world model, a search, etc. the kind of stuff that actual AIs, even a tik tac toe AI, have, but LLMs don't.

On top of it this all works through machine learning, which produces the resulting network weights through very gradual improvement at next word prediction, tiny step by tiny step. Even if some sort of discrete model (like say the account of what's on either side of the river) could help it predict the next token, there isn't a tiny fraction of a discrete "model" that would help it, and so it simply does not go down that path at all.