##### 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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Tuesday, July 17, 2007 at 4:57 pm

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

Tuesday, July 17, 2007 at 5:05 pm

Abe, 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.

Tuesday, July 17, 2007 at 5:08 pm

Feel 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).

Tuesday, July 17, 2007 at 10:02 pm

Well, 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.

Wednesday, July 18, 2007 at 11:13 am

I 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.

Wednesday, July 18, 2007 at 4:11 pm

I guess that means 19 minutes is incorrect 😦

Wednesday, July 18, 2007 at 4:22 pm

19 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.

Thursday, July 19, 2007 at 10:06 pm

Yay 😉

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Wednesday, July 25, 2007 at 6:23 pm

A&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.

Wednesday, November 21, 2007 at 12:14 am

No, 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).

Thursday, December 20, 2007 at 3:59 am

I 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.

Tuesday, January 15, 2008 at 9:08 pm

17 min is correct!!

Wednesday, October 29, 2008 at 4:58 pm

A good way eh? Are you trying to reach my purple chart Fresh joke! What geometric figure represents a lost parrot? A polygon.

Saturday, December 13, 2008 at 5:36 pm

Thanks!,

Sunday, February 8, 2009 at 12:43 am

I have a more efficient answer 14 min.

Runner 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!