Someone emailed this puzzle to me claiming that he'd received it from someone else. The original message claimed that it was a Microsoft interview question, and the interviewee gets 10 minutes to figure out the answer. No answers were provided with the email, but he's what I (and others) have come up with.
1.) As a purely mathematical problem, it is a variant of Xeno's (or is that Zeno? but definitely not Xena) paradox. Here's how it goes:
....A == 10 min/bridge length
....B == 5 min/bridge length
....C == 2 min/bridge length
....D == 1 min/bridge length
....A and B should walk together as much as possible without
....backtracking. So first divide the bridge length into quarters:
....D & A 1/4 bridge length == 2.50 min
....D returns.............. == 0.25 min
....D & B 1/4 bridge length == 1.25 min
....D returns.............. == 0.25 min
..............................----------
.............................. 4.25 min, so far so good
....Their physical arrangement is
.....|------|------|------|
....C&D....A&B
....Now shift them all down 1/4 length:
....D & C 1/2 bridge length == 1.00 min
....D returns to A & B (1/4)== 0.25 min
....A & B to C (1/4 length) == 2.50 min
....C returns to D......... == 0.50 min
..............................----------
4.25 min for a total of 8.50 min
.....|------|------|------|
...........C&D....A&B
....If you do this two more times, A & B reach the end of the
....bridge in 17.00 min (=8.50+2*4.25), but C & D are still 1/4
....of the way from the end.
.....|------|------|------|
..................C&D....A&B
....So it takes a grand total of 17.5 minutes to get them all
....across. It turns out that as you divide the bridge into
....smaller and smaller units, it always takes 17.0 minuntes to
....get to the configuration in which A & B are at the end of
....the bridge and C & D are some distance from the end, so the
....shortest time can approach 17.0 minutes, but never quite get
....there.
2.) A couple suggested "Microsoft/Bill Gates" answers:
....a. D teams up with C to bludgeon A and B to death with the
...... flashlight and rifle their pockets for cash. Having been
...... successful in this task by obtaining C's help, D then
...... bludgeons C to death as well and takes all the cash.
...... 16 minutes for three bludgeonings and lootings is plenty
...... which leaves the required 1 minute for D to cross the
...... bridge.
....b. The team tries to cross by the above method, figuring that
...... 17.5 minutes is close enough to 17.0. However, the
...... batteries to the flashlight expire when they are all part
...... of the way across. This is a bug which will be fixed in
...... V1.2. By V2.0 all four will have flashlights, and Xeno95
...... (which should be out any time now) will include a lighted
...... bridge.
joule