The hobbits and orcs problem

There are several solution paths for the hobbits and orcs problem¹. The following table shows one of them (b = boat, H = hobbit, O = orc):

Step	Starting bank	Journey	End bank
start	bHHHOOO
1	bHHOO	bHO →
2	bHHOO	← bH	O
3	bHHH	bOO →	O
4	bHHH	← bO	OO
5	bHO	bHH →	OO
6	bHO	← bHO	HO
7	bOO	bHH →	HO
8	bOO	← bO	HHH
9	bO	bOO →	HHH
10	bO	← bH	HHOO
11		bHO →	HHOO
12			HHHOOO

There is a particular point in this solution path where people get into difficulties, and that is Step 6. At this point the action that needs to be taken is to move one creature of each type back to the first side of the river. This seems to be decreasing the similarity between current state and goal state, hence conflicts with the difference reduction heuristic. Consequently, about a third of participants prefer to go back to Step 5².

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Footnotes

1. The original version of this problem was known as the "missionaries and cannibals" problem, though this wording is less frequently used now.

2. Jeffries, R.P., Polson, P.G., Razran, L., & Atwood, M.E. (1977). A process model for missionaries: Cannibals and other river-crossing problems. Cognitive Psychology, 9, 412-440.