Weekly Riddle: The Runners
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Tuesday, July 17, 2007, 12:45 pm
Filed under: riddles & puzzles
Filed under: riddles & puzzles
So I think I am gonna start posting weekly riddles. Its fun, its educating, and I like the challenge. And I consider you, my peers, to be like-minded so I assume you enjoy riddles too. Please keep in mind that others might want to challenge themselves so please refrain from posting your answers in the comments. Instead, I will post the answer on next week’s weekly riddle.
This week: The Runners…
The facts:
- There are four runners.
- It is dark.
- There is only one flashlight.
- There is a bridge spanning a huge crevasse.
- The bridge can only sustain two people at any one time (its old, long, and creeky).
- It is necessary to traverse the bridge with a flash light.
- The crevasse is too wide and far to toss the flash light across, or otherwise transport it by any means other than by crossing the bridge.
- Runner A can cross the bridge in 1 minute.
- Runner B can cross the bridge in 2 minutes.
- Runner C can cross the bridge in 5 minutes.
- Runner D can cross the bridge in 10 minutes.
- This is set in reality meaning the runners have no James Bond-ish gadget for such an occasion.
The goal:
- What is the shortest amount of time to get all four runners across the bridge?
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hi,
well 10 min. assuming runner 10 holds the light, once one person has finished the crossing the next can start immediately so long as there is never more than 2 at one time on the bridge.
so runner 1 and 4 start
runner 1 will be done in 1 min after that runner 2 starts
2 min later runner 3 starts
1-3 will finish in 8 min
runner 4 finishes in 10 (4 holds the light as he is always on the bridge.
abe
Comment by abe Tuesday, July 17, 2007 @ 4:57 pmAbe, a noble attempt but it doesn’t fit within the constraints of the riddle.
Since a flashlight is necessary to traverse the bridge, in your solution, runner number 1 would be crossing without a flashlight once leaving runner 4 in the dirt, inadvertently losing his footing and falling to his demise in the crevasse. Any subsequent runners who do the same (since runner 4 is the slowest) would also fall off the bridge. So only 10-minute Tubby would make it across.
Comment by jwopitz Tuesday, July 17, 2007 @ 5:05 pmFeel free to comment and chime in with your solutions, however, I am moderating them so as to not reveal (and spoil) the riddle until next week’s riddle.
So basically only wrong answers will be allowed on the weekly riddles’ comments (so as to learn from others’ mistakes).
Comment by jwopitz Tuesday, July 17, 2007 @ 5:08 pmWell, I’d go for 19 minutes, assuming two people have to traverse the bridge together holding the flash light. Runner 1 will have this job, and unfortunately for him this means the poor fellow clears the bridge 5 times, simply becasue he can return the flashlight to the other site in the shortest amount of time.
Comment by Tiemen Tuesday, July 17, 2007 @ 10:02 pmI get 19 minutes.
Step 1: Runners #1, #4 go across (10 mins) and #1 comes back (1 min).
Step 2: Runners #1, #3 go across (5 mins) and #1 comes back (1 min).
Step 3: Runners #1, #2 go across (2 mins).
Total: 19 minutes.
Comment by Ed Wednesday, July 18, 2007 @ 11:13 amI guess that means 19 minutes is incorrect
Comment by Ed Wednesday, July 18, 2007 @ 4:11 pm19 minutes is not the correct answer. But the approach that both you (Ed) and Tiemen used is the correct approach.
19 minutes is the typical answer.
Comment by jwopitz Wednesday, July 18, 2007 @ 4:22 pmYay
Comment by Tiemen Thursday, July 19, 2007 @ 10:06 pm[...] ANSWER TO LAST WEEK’S RIDDLE: The Runners: [...]
Pingback by Weekly Riddle: An Angle on a Cube « jwopitz - flex/flash exploration Wednesday, July 25, 2007 @ 3:08 amA&B start over the bridge together with B holding the light. A reaches the other side in one minute. B turns back. Time = 2 min.
B&C start out together with C holding the light. B reaches the other side in 2 min. C turns back. Time = 4 min.
C&D start out together with D holding the light. C reaches the other side in 5 minutes followed by D five minutes later. Time = 10 min.
Total time to get all four across the bridge = 16 min.
Comment by Charles Wednesday, July 25, 2007 @ 6:23 pmNo, you got it wrong too Charles. Right answer (16) but wrong solution as the first journey plus return takes 4 mins if you do it your way (charles).
Here is a hint – the correct soln involves A and B crossing the bridge together twice (as well as seperately).
Comment by chaz Wednesday, November 21, 2007 @ 12:14 amI got 17 minutes.
A and B cross together. 2 minutes
A goes back by his self. 1 minute
C and D cross together. 10 minutes
B goes back by his self. 2 minutes
A and B cross together. 2 minutes.
2+1+10+2+2=17
It doesn’t matter whether A or B goes back in the second step as the other one will have to cross by them self later. I don’t think you can do it in 16 minutes.
Comment by Alex Thursday, December 20, 2007 @ 3:59 am17 min is correct!!
Comment by tin Tuesday, January 15, 2008 @ 9:08 pmA good way eh? Are you trying to reach my purple chart Fresh joke! What geometric figure represents a lost parrot? A polygon.
Comment by Jobelayelay Wednesday, October 29, 2008 @ 4:58 pmThanks!,
Comment by Fletvfew Saturday, December 13, 2008 @ 5:36 pmI have a more efficient answer 14 min.
Comment by aifaov Sunday, February 8, 2009 @ 12:43 amRunner A & Runner B go together 1st 2 min.
Runner A returns 1 min
Runner C & D cross 10 min
& because Runner A already knows the path (he had crossed twice already), he is able to cross w/o the flashlight!