## Puzzle : Cross the bridge

Well,

This is yet another cross-the-bridge puzzle. This puzzle was posted on our group list by my friend Manoj Gupta. Without circling around, let me directly come to the point.

Problem :

M – Mother

F – Father

s1, s2 – sons

d1,d2 – daughters

P – Policeman

T – Thief

They are all standing at one side of the bridge. There is only one car with the capacity of two people. Only M, F or P can drive. The catch is that the father is hostile towards the daughters, and mother is hostile towards the sons. So if the mother is not there to protect the daughter, the father would kill them even he gets this chance for a second.  Similarly, if father is not around to protect the son, mother would kill the sons. And when policeman is on the other side of the bridge, the thief would kill everybody on the same side of the bridge as his. How can they all cross the bridge safely ?

Solution : Following is the state sequence that would give the trace how we can move everybody safely to the other side.

```MFs1s2d1d2PT = _ ( Initial configuration )
MFs1s2d1d2 = PT ( Police drives thief to the other side )
MFs1s2d1d2P = T ( P comes back )
MFs1s2d1 = PTd2 ( P drives d2 to other side )
MFs1s2d1PT=d2  ( P comes back with T )
Fs1s2PT=Md1d2 ( M drives d1 to the other side )
MFs1s2PT=d1d2 ( M comes back )
s1s2PT=MFd1d2 ( M drives F to the other side )
Fs1s2PT=Md1d2 ( F comes back )
Fs1s2=Md1d2PT ( P drives T to the other side )
MFs1s2=d1d2PT ( M comes back )
s1s2=MFd1d2PT ( M drives F to the other side )
Fs1s2=Md1d2PT ( F comes back )
s2=Fs1Md1d2PT ( F drives s1 to the other side )
PTs2=Fs1Md1d2 ( P comes back with T )
T=Fs1s2Md1d2P ( P drives s1 to the other side )
PT=Fs1s2Md1d2 ( P comes back )
_=Fs1s2Md1d2 ( P drives T to the other side )

I have seen earlier puzzle when you have to cross the river with Tiger, Goat and Grass
but I guess this one has more constraint.

--Saurabh Joshi
```

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### 3 Responses to “Puzzle : Cross the bridge”

1. Manas Paldhe Says:

Alternative solution…
Similar until:
s2=Fs1Md1d2PT ( F drives s1 to the other side )
PTs2=Fs1Md1d2 ( P comes back with T )
T=Fs1s2Md1d2P ( P drives s1 to the other side )
PT=Fs1s2Md1d2 ( P comes back )
_=Fs1s2Md1d2 ( P drives T to the other side )

In the alternate solution.
s2=Fs1Md1d2PT ( F drives s1 to the other side )
FMs2 = s1 d1 d2 P T (F driver M to original side)
M= F s2 s1 d1 d2 P T (F drives s2 to other side)
FM= s2 s1 d1 d2 P T (F returns)
0= FM s2 s1 d1 d2 P T (FM go across)

• Saurabh Joshi Says:

Hi,
The alternate solution provided by you is flawed. The reason is that when you reach a state where M=Fs2s1d1d2PT the father would kill the daughters. The policemen only prevents the thief from killing everybody else. For the daughters to survive, mother has to be present when father is present.

2. Manas Paldhe Says:

Oh! Yes.
Sorry did not verify the solution properly,