Two strong-man competitors, Atlas and Brutus, are smashing large rocks with great blows of a hammer. Their goal is to smash as many rocks as they can with four strikes. They each get one point for each crumbled rock.

An unstruck rock has a 20% chance of crumbling, a rock that has been struck once but didn't crumble has a 40% chance of crumbling on its second strike, a rock struck twice has a 80% chance of crumbling on its third strike, and a rock that survives 3 strikes is guaranteed to crumble on the fourth.

What is the probability that the final score is a tie?

Note: This problem is highly adapted from a regional math competition for students up to grade 9 and calculators were not allowed. The solution was requested to two decimal places.

Do they take turns on the same rock, since, otherwise, won't 4 blows from one man would always guarantee him a point? Who goes first? Or do they handle their own rocks separately... (a fixed number of rocks, maybe with a final success tally)? Or maybe it's a speed contest? 

Posted by Steven Lord on 2023-05-08 11:59:44