This Game is meant for Boy Scouts, Webelos scouts.
Decide for yourself if it is appropriate for your younger scouts or not.

long straight stick such as a broomstick

Two opponents, of similar size for fairness, hold stick at full height over their heads.
On 'Go' signal, both scouts try to twist the stick in the grip of the other.
The stick can be lowered and raised.

When the judge gives 'STOP' signal, scouts stop immediately and let the judge determine how the stick has twisted. Marking the stick with a notch on top or a line of paint will help.

You may add the rule that a scout can not move his feet.

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Alternative: Each scout holds the stick with two hands so the stick is perpendicular between the two and horizontal. The object is to push the other scout's left side of the stick to the ground while keeping his own left side off the ground. First to touch the ground wins - play best of three tries.