Four persons are standing in front of a canyon. The only
bridge can carry only two persons at once. Because of
the darkness the persons have to use a torch.
Unfortunately there is only one torch. Whenever two
persons have crossed the bridge one person must carry
back the torch. Person A needs 5 min for crossing the
bridge (one way). B needs 10 min, C needs 20 min and
D needs 25 min. Two persons together need the time of
the slower one.
What is the minimum time for the group to cross the bridge?
Correct answer: 60 minutes (1 hour)
Explanation:
ABCD
CD -- AB --> : takes 10 min.
CD AB
CD <-- A --- B : takes 5 min.
ACD B
A -- CD --> B : takes 25 min.
A BCD
A <-- B --- CD : takes 10 min.
AB CD
-- AB --> CD : takes 10 min.
ABCD
=========================================================
60 min.
One very common WRONG solution is this:
ABCD
CD -- AB --> : takes 10 min.
CD AB
CD <-- A --- B : takes 5 min.
ACD B
D -- AC --> B : takes 20 min.
D ABC
D <-- A --- BC : takes 5 min.
AD BC
-- AD --> BC : takes 25 min.
ABCD
=========================================================
65 min.
