For the 8-puzzle, suppose:

• h₁(n) = 0 (defaults to breadth-first search)
• h₂(n) = number of tiles out of place in n
• h₃(n) = sum of distances out of place in n
• h*(n) = actual distance to goal from n

Then:

h₁(n) ≤ h₂(n) ≤ h₃(n) ≤ h*(n)

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