SUBJECT>Re: some solutions -- better diagrams POSTER>joule EMAIL>@the.lab DATE>March 18, 1997 at 21:24:51 EMAILNOTICES>no PREVIOUS>1326 NEXT> LINKNAME> LINKURL>
Ack! I forgot that periods won't work to line things up. Here are the bridge diagrams again:
2.50 min == D & A to 1/4 bridge length
0.25 min == D returns
1.25 min == D & B to 1/4 bridge length
0.25 min == D returns
--------
4.25 min == so far so good
Their physical arrangement is
C------A------|------|
|------|------|------|
D------B------|------|
Now shift them all down 1/4 length:
1.00 min == D & C to 1/2 way point
0.25 min == D returns to A & B (1/4 length)
2.50 min == A & B to C (1/4 length)
0.50 min == C returns to D
--------
4.25 min ==> 8.50 min total
|------C------A------|
|------|------|------|
|------D------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------A
|------|------|------|
|------|------D------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.