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.
(In reply to
would like to understand the contest better.... by Steven Lord)
my interpretation - no spoiler
I'm about to post my solution.
I assumed that each one keeps hitting a rock until it explodes, then moves on to another rock.
Doing otherwise would worsen their chances.
In an earlier version of the problem there were points, one point for each rock crumbled. So I assumed the number of rocks smashed is the score.
I assumed speed was not a factor.
|
|
Posted by Larry
on 2023-05-08 12:48:13 |
re: would like to understand the contest better....
