A mother (210 pounds), son (80), daughter (65) and a bowling ball (50) must escape a tower by a pair of...
decision/crossing/tower.pulley New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
A mother (210 pounds), son (80), daughter (65) and a bowling ball (50) must escape a tower by a pair of baskets on a pulley that may not be unbalanced by more than fifteen pounds. How? A mother (210 pounds) and her son (80 pounds) and daughter (65 pounds) are trapped in a tall castle with their bowling ball (50 pounds) and need to escape. There is a pair of baskets supported by a pulley outside their window, so that one basket is up while the other is down on the ground. They want to take turns lowering each other to safety, but know that if the baskets are out of balance by more than fifteen pounds, the mechanism will move at a dangerous pace and riders will be seriously hurt. What sequence do they use to escape? -- David Roche <droche@innocent.com>
Show solution
Uhm, they don't have anything that's at most 15 pounds, so there's no
escape unless someone gets seriously hurt.
Oh, you mean the bowling ball is allowed to get hurt? How cruel.
In that case:
MSDB MSD MSB MDB MD
----+ ----+ ----+ ----+ ----+
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| |B |D |S |SB
+---- +---- +---- +---- +----
MB M SDB SD SB
----+ ----+ ----+ ----+ ----+
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
|SD |SDB |M |MB |MD
+---- +---- +---- +---- +----
DB D B
----+ ----+ ----+ ----+
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
|MS |MSB |MSD |MSDB
+---- +---- +---- +----
Of course, that's under the assumption son, daughter and bowling ball
fit in a basket, the entire system holds 405 pounds, and a bowling ball
flying down doesn't hurt anyone.
-- Abigail <abigail@fnx.com>
[ Editor: M = mother, S = son, D = daughter, B = bowling ball; each
picture shows who is up in the tower and who is on the ground. The
only rides with people aboard are D (65) down against B (50), S (80)
against D (65), and M (210) against S+D+B (195), each within 15
pounds; the ball goes down alone in between. ]