The bears managed to collect quite a haul of conkers, but then couldn't think what to do with them?
Scary told them about a game you can play with conkers. It involves very carefully boring a hole through the conkers (they would need to let Jane help them with that). Then a knot is tied at the end of a length of string, and this is threaded through the conker until it stops at the knot. If you don't have any string, you could use shoelaces. Every player would need their own conker made the same way.
The idea of the game is that two players, each with a conker threaded on a piece of string, take it in turns to hit each other's conker, until one is completely destroyed (though the winning conker might end up looking very battered too!)
One player holds out their conker at arm's length, hanging down, ready to be hit. The string is wrapped around their paw, to stop it being dropped.