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### Cross Bridge Puzzle

Cross Bridge Puzzle - 26 july

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

1. its 24. you didnt take into account all of the times the 1 min. person would have to walk back with the torch

2. 10 for the first trip, 10 and 1 go together.
1 for him coming back
7 for the next trip
1 for him coming back
2 for the last trip
10+1+7+1+2= 21

3. 17mins is the correct answer

1. 21 is wrong

2. 17 Mins

3. 17 mins is correct.

4. It will take only 10 minutes. The one who takes 10 minutes and the one who takes 7 minutes will start crossing the bridge. When the second person has crossed after 7 minutes, the third person who can cross in 2 minutes will cross and then the one who can cross in 1 minute. At a given time only two persons will be on the bridge and by 10 minutes all would have crossed.

1. wrong, the torch is meant to bind 2 people together

2. yup...the answer is wrong....it is 17 mins.....1 and 2 go first.....then 1 comes back....then 7 and 10 go....and 2 comes back...then 1 and 2 go again....it makes a total of 17 minutes..!!!

5. The 10 minute answer is wrong ... as the last two people would not have the needed torch. 17 minutes is.

The fastest pair cross then either of them returns after which the slowest pair cross and the one who remained the first time returns for the one remaining person from the other side.

10 minutes for the slow pair, and of the others the second slowest crosses three times and the fastest once alone 10 plus 3 times 2 plus 1 is 17.

1. 10 mins....
it is correct the slowest remember the path and give light to the 2 min and 1 min people

6. 10 min. only
life is simple,don't make it complicated....

1. man this is question of logic not of philosophy

7. 10 min is wrong

8. The 10 minute answer neglects the fact they need the torch to cross, therefore it is always only one crosser, or two side-by-side, sharing the torch.

9. bang on target......17 mins :-)

10. VEERA
1m+2m travel first 2m
1m or 2m return 1m (2m)
10m+7m travel next 10m
2m or 1m return 2m (1m)
2m+1m travel finally 2m
17m

1. good one....

2. yes ur right

11. Total 10 min

10min and 7min person start with the torch in 10min person hand...

at time t=7min :
10 min person is 3 min away from completing the bridge with a torch in his hand and 2min person joins him...

at time t=9min :
10 min person is 1 min away from completing the bridge with a torch in his hand and 1 min person joins him

at time t=10min :
both 10 min person and 1 min person exit the bridge..

THUS THE ANSWER IS 10 MINUTES !!!

1. U neglected the fact that they need a torch always

2. Although the reason for having the torch is neglected ( all peopl need like to see the bridge) The rule is not technically broken the torches on the bridge the entire time and there's no more than two people the entire time.

3. How did the 2min person join the 10min person? Either they all broke the bridge (too heavy) or 2min person fell through the bridge walkway because THEY COULDN'T SEE the BRIDGE! (no torch, it was three minutes away)

12. Are you guys being stupid on purpose? The question CLEARLY states that only two people can be on the bridge at any one time. Yet, the people answering 10 minutes have more than 2 people on the bridge at any one time.

1. we are also satisfiyng 2 people's criteria...

13. 10 mins,
If they are not side by side but the torch is in the 10 min guy hand on the bridge.
10 mins guy has the torch lighting it up the bridge. While 1,2, and 7 min go by one at a time. Satisfying only 2 people on the bridge.
10 mins is the fastest... Time.

13 mins is second fastest..
If Needed to be side by side but statisfying just needed to cross the bridge.
but not having all on the same side at one time.
1m and 2m cross time 2min. Now 1and 2 min guy has cross the bridge
1m returns torch. Time 1min. Gives it to 10 and 7 min guys
10 and 7 min cross time 10min
Total 13 min, if statisfying 1 min guy cross the bridge already.

17 min is third fastest
Side by side and all has cross and other side of the bridge at sime time.

If Needed to be side by

14. All they need is 5mins.. because "they cant cross without one".. here the one means torch so the two crossing need light and the question didn't mentioned about their weights.. so the person whose time is 1min carries the remaining three who hold the torch.

first routine: 1 carries 10 = 1min
he returns = 1min
Second routine: 1 carries 7 = 1min
he returns = 1min
Third routine : 1 carries 2 = 1min

so totally 5 mins

1. 3 min

1min carries 7min or 10min
2min carries 10min or 7min

:)

2. Torch has to b bought back na for rest two to cum

3. If the one min could hold all three then it takes 1 minute but if normal then 17

15. with 1 minute guy carrying the 10 & 7 minute guy, can't he 2 minute guy be on the bridge carying the 7 minute guy. still only two pair of feet on the bridge, and it only took 2 minutes.

1. its 12 minutes 10+2=12

16. time to build new bridge

17. Thought the answer was 17 but explanation for 20 makes absolute sense

18. new bridge with lights! swimming lessons are important too..

19. do we have an answer?

1. http://solution-dailybrainteaser.blogspot.in/2011/07/cross-bridge-puzzle.html

20. 10,7,2,1 ------------------ >>
BRIDGE
10,7 ------------------- >> 2,1 Time =(2)

10,7,1 <<-------------------- 2 time =2+1

1 ---------------------- >>> 10,7,2 time = 2+1+10

2,1 <<------------------- 10,7 time =2+1+10+2

---------------------------------->>> 10,7,2,1

Final time = 2+1+10+2+2

1. 20 minutes...in my opinion. Here's my thought:
The fastest person can stand in the center of the bridge and hold up the torch(Up to 1min trip).
The slowest person safely crosses the bridge first
(10min trip).
The second slowest follows after(7min trip).
The second fastest meets up with the fastest person,then follows him the rest of the way
(2min trip).

21. two persons(one takes 1 min and other takes 10 min) started->one min guy crossed , returned(gave torch to 2 min guy)->(took 3 min)->time elapsed(1+1+1).
after reaching of one min guy,2 min guy started,crossed, gave torch to 1 min guy who again came back to give torch to 7 min guy and went back-> time elapsed(3+2+1+1)
7 min guy started, the 10 min guy reached 7-3 = 4 seconds before the 7 min guy. Now total time taken for everyone to cross the bridge-> 7+7=14 min

1. correction for seconds...all time units are in minute here.

22. 10 min is totally wrong!answer is 17
1st route we will take 1 and 2 and leave 2 across the bridge and again take 1 back(3min)
2nd round we will take 7 and 10 (10min)and take 2 back
(2min)and in last we will take 1 and 2(2min)
total time 3+10+2+2=17min

23. 21 min is the shortest time for all to cross safely.

10 min guy holds touch and crosses in front of 1 min guy causing him to slow down, = 10 min. 1 min dashes back across and gives torch to 7 min guy who now leads 1 min guy back across bridge = 8 min. 1 min dashes back across and gives torch to 2 who leads 1 min guy back across bridge = 3 min.

10 + 8 + 3 = 21 min

Here we see how is it.

1st travel: 2people(1min and 2 mins) crossing takes 2mins.
one of them have to come back to give the torch for other 2. so 1min person is coming back. now 2mins+1min for coming back takes 3mins.

2nd travel: 2people(7mins and 10mins) are crossing. it will take 10mins to cross for both of them. 3mins+10mins=13mins. now another person is standing other side of the bridge. for that person to cross the bridge one person among the has to go other side with torch. 2mins person is taking the torch and moving to other side. (13mins+2mins=15mins)

3rd travel: Finally two persons(1min and 2mins) are crossing the bridge. 15mins+2mins=17mins.

All are in the other side now,,,,.

thats all. cool

25. 17 is right without any assumptions. But since all the ppl take different times to cross the same bridge, its probably because they are too scared to cross it. Assuming its a short bridge and seeing as we are gunning for shortest time with 2 people crossing at a time, its possible for the 10 7 pair to cross first and then throw the light back to the next pair on the other side for a near 12 minute run.

26. 10min ans is wrong....the bridge can support only 2 at a time!

27. 10 minutes,,,let the 4th person and the 1st person starts the journey..it takes 1 minutes to cross the bridge by 1st person and the time remaining is 9min for 4th person..in the mean while the 2nd person starts and completes in 2 mins and 7 mins are still in hand of the 4th person.then the 3rd person starts and both finishes together...

28. 17 is correct

29. It's really simple. Let's just say the A croses in 1 min B 2 C 5 and D 10
1. A and B go(3 min)
2. B OR A can return(doesn't matter. Let's just say A)
3. A gives flashlight to D and C(10 min)
4. B comes back(1 min)
5. They cross together again(2 min)
3+1+10+1+20=?

1. A+B=2 minutes
B returns=2 minutes
C+D=10 minutes
A return= 1 minute
A+B= 2 minutes
2+2+10+1+2=17 minutes.
You were adding the minutes. If it takes one person 2 minutes to cross and the other 1 minute, if they go together it only takes 2 minutes, not 3.
Therefore, 17 is the correct answer.

17 mins

The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 mins. Is that it? No. That would make this question too simple even as a warm up question.

Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.

1 and 2 go cross
2 comes back
7 and 10 go across
1 comes back
1 and 2 go across (done)

Total time = 2 + 2 + 10 + 1 + 2 = 17 mins

31. 17 min because 1 and 2 go,=2, 1 comes back = 3, 7 and ten go = 13, 2 comes back = 15 and 1 and 2 go back =17

32. it would be 12 do the math dur

33. ITS 17 mins

34. 5 minutes. Have the person who only takes a minute carry the others. it will take them 5 crossings to bring the other three across. each trip taking only a minute. The person carried can hold the torch.
there is no mention of the integrity of the bridge being too suspect to support a concentrated weight.

35. the answer has to be more then 10 min intially, because the person that needs 10 minutes to cross the bridge will take that time. Since there are more than two people and the bridge only takes two at a time, there will be automatically more than 10 min wasted and at least 4 trips.

1 takes 2 with him - 2 waits on the other side - 2 minutes wasted.
1 comes back to 7 and 10 - 3 minutes wasted.
7 and 10 cross the bridge, leaving 1 waiting for the torch to cross the bridge - 13 minutes wasted.
2 comes back to 1 with the torch - 15 minutes wasted.
2 and 1 cross the bridge - 17 minutes wasted.

36. 21 minutes

37. 10 and 7 go together = take 10 mins
1 and 2 go together = take 2 mins

total time: 12 mins

38. Them answer is 13 if you answer them question directly. 1&2 cross and 1 returns. Then 10&7 cross. 2+1+10=13. It just asked how long for them to all cross them bridge. At this point they all have crossed, even though the 1 minute man is at the original side. He did cross, he's just not on them same side as them other three.

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40. 17 mins!!!!!!!!

41. MOLS: Members on Left side
OTB: On the bridge
TT: Travel Time
MORS:Members on Right side

MOLS OTB TT MORS
10,7 1,2 3 2
1 10,7 12 10,7
1,2 2
Total Time 17

Thus the shortest time is 17 min

1. 12mins is the shortest time
10 and 7 cross with the light first
1 and 2 are on the other side waiting for the light

42. .00000000000001 seconds

43. 25 min to cross the bridge. First 1 min & 2 min will go. They would take 2 mins. Then 2 min person will go and bring 7 min person(it would take 9 min[2+7]). Then 7 min person will go & bring 9 min person. It would take 16 min I.e.7+9. Therefore the total is 2+7+7+9.

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