Solution to the Problem
This game is solvable even if there are 4
pairs, 5 pairs or more pairs of penguins,
the point is to get the pattern right.
First, move a small penguin to the ice, and
then its parent, move them to the opposite
shore:

Move the small penguin back:

Move another small penguin to the ice, and
move them to the opposite shore:

Move the first small penguin to the land,
and move the ice back:

Move the small penguin's parent to the ice,
and then move to the opposite shore:

Leave the parent behind and move back:

Follow the same pattern and you can move all
the penguins to the opposite shore:


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