Help figuring a riddle

[TDY2KN01]

My friend has a riddle which was given by his teacher for extra credit. I can't figure it out, but I know there are alot of smart people coming to this board. Here is the porblem. there is a bridge and there are four people, and they each take different amounts of time crossing the bridge. A takes 1 minute, B is 2 minutes, C is 5 minutes and D is 10 minutes. The goal is to get them all across in 17 minutes or less. Here are the rules: It is night time and only two people at a time can cross the bridge at a time. Since it is night time, one person crossing the bridge needs a flash light at all times. So here is an example since this is hard to explain through writing. person A and C go cross the bridge, this is 5 minutes (the time of the slowest person) and A or C must cross the bridge again with the flashlight. so person A goes back, this is 1 minute. Now A and B decide to cross the bridge together this is 2 minutes, then A goes back and this is 1 minute. then A and D go together this is 10 minutes. Now they are all on the other side, but it adds up to 19 minutes. try to get it to seventeen minutes or under.

 

[fatbaby]

d takes c, c leaves d and goes back and takes b, b leaves and goes and takes a.

1+2+5+10=18! only 1 minute off.

oops are you sure its both ways?

took me 2 min to guess this:

c takes b, then b leaves c and takes a, then a leaves and takes d.
5+2+10=17!

 

[AreaCode707]

No rule says they all have to wind up on the same side of the bridge, they just all need to cross it at least once. And where does it say they have only one flashlight?

 

[McPhreak]

<< d takes c, c leaves d and goes back and takes b, b leaves and goes and takes a.

1+2+5+10=18! only 1 minute off. >>



That's actually 24 minutes. You forgot to add the time going back.

 

[Talon]

A and B over = 2 minutes
A comes back = 3 minutes
C and D over = 13 minutes
B comes back = 15 minutes
A and B over = 17 minutes

 

[McPhreak]

<< A and B over = 2 minutes
A comes back = 3 minutes
C and D over = 13 minutes
B comes back = 15 minutes
A and B over = 17 minutes >>



We have a winner!

 

[ungsunghero]

Seventeen minutes:

A + B go...2 minutes
A goes back...1 minute
C + D goes...10 minutes
B goes back...2 minute
A + B go again...2 minutes

2+1+10+2+2 = 17 minutes

Darn...looks like I got beat to it.

 

[Lithium381]

<<

<< A and B over = 2 minutes
A comes back = 3 minutes
C and D over = 13 minutes
B comes back = 15 minutes
A and B over = 17 minutes >>



We have a winner! >>



yay *busts out the party hats*

 

[Talon]

Someone here posted a link to a series of 4 flash games recently. This was one of them only with more characters and different times. Same strategy.

 

[Lithium381]

<< Seventeen minutes:

A + B go...2 minutes
A goes back...1 minute
C + D goes...10 minutes
B goes back...2 minute
A + B go again...2 minutes

2+1+10+2+2 = 17 minutes

Darn...looks like I got beat to it. >>



btw - welcome to anandtech ungsunghero!!!

 

[TDY2KN01]

to talon, THANK YOU VERY MUCH. it was an ec prolem, and it was worth a lot. thankjs very much