Yikes.
Labeling us 10, 5, 2 and 1 by how long we take to cross
the bridge — always with
lantern L — each forward crossing
will have two of us, taking as long as the slower one.
Each return crossing will be made by someone alone.
Elapsed Side of Crossing Side of
Narrative Time Peril (minutes) Safety
-------------- --------- ------------ ----------- -------------
We arrive 0 10 5 2 1 L
1+2+L cross 10 5 1 2 L (2)
2 10 5 L 1 2
1+L returns 10 5 1 L (1) 2
3 10 5 1 L 2
10+5+L cross 1 10 5 L (10) 2
13 1 L 2 5 10
2+L returns 1 2 L (2) 5 10
15 1 2 L 5 10
1+2+L cross 1 2 L (2) 5 10
Zombies arrive 17 Zombies L 1 2 5 10
Whew!
Now safe, the story of temptation and resistance may be told.
This resisted the temptation to have the quickest cross each time,
minimizing every return trip.
Having 5 and 10 cross together, instead,
more than made up for a return trip made by 2 instead of 1.
In fact 5 could have been a second 10 and been just as safe.
Here is how a panicked
scramble — where the quickest always crossed
first — would have ended in tragedy.
It would have taken 19 minutes to complete,
with the zombies causing the bridge to collapse
while 1 and 10 were still 2 minutes from safety:
Elapsed Side of Crossing Side of
Narrative Time Peril (minutes) Safety
-------------- --------- ------------ --------------------- ---------
We arrive 0 10 5 2 1 L
1+2+L cross 10 5 1 2 L (2)
2 10 5 L 1 2
1+L returns 10 5 1 L (1) 2
3 10 5 1 L 2
1+5+L cross 10 1 5 L (5) 2
8 10 L 1 2 5
1+L returns 10 1 L (1) 2 5
9 10 1 L 2 5
1+10+L begin 1 10 L (8) 2 5
Zombies arrive 17 Zombies 1 10 L (2 to go) 2 5
And this how a well-mannered
approach — where the slowest
went earlier— would have played out horrifically.
It would also have required 19 minutes to complete
but has the zombies arriving
just as 1 returns to be a brain meal along with 2,
who never even got moving:
Elapsed Side of Crossing Side of
Narrative Time Peril (minutes) Safety
-------------- --------- ------------ -------------- ------------
We arrive 0 10 5 2 1 L
1+10+L cross 5 2 1 10 L (10)
10 5 2 L 1 10
1+L returns 5 2 1 L (1) 10
11 5 2 1 L 10
1+5+L cross 2 1 5 L (5) 10
16 2 L 1 10 5
1+L returns 2 1 L (1) 10 5
Zombies arrive 17 Zombies 2 1 L 10 5
In both of these less fortunate approaches,
5 would have had to be a 3 or quicker
to allow for a happy ending.
