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## Question

A puzzle I got from a very old man while traveling, quite a while ago. It reminded me of a Lewis Caroll puzzle, though the settings are very different!

Anyway, here is the puzzle:

Once upon a time, A king and his wife, the minister and his wife, and the servant and his wife were traveling. They came to a river, where a boat stands. Now there are a few rules one must remember:

1. Not more than 2 people can travel at a time in the boat.

2. King, his wife, Minister and his wife consider themselves as high class. So they cannot travel with the servant or his wife.

3. None of the men have faith on their wives (or any of the other men!), so they cannot leave their wives in the company of any other men EVEN FOR A SECOND! (for example none of the men can leave their wives alone with the any of the other men, even if their wives are around) Also note the class doesn't matter in this case! So even the servant wont allow the King to have his way with his wife. Proud man he is!!

So tell me the way in which they cross the river, so that it requires minimum possible commutation?

k - king, m - minister, s - servant

kw - king's wife, mw- minister's wife, sw - servant's wife

() notation for those travelling across

[] notation for those returning

This side - the starting side of river

Across - The other side of river

Solution:

This side: k, kw, m, mw, s, sw

This side: k, kw, m, mw

Across: (s), (sw)

This side: k, kw, m, mw,

Across: sw

This side: k, m, s

Across: (kw), (mw), sw

This side: k, m, s, [sw]

Across: kw, mw

This side: s, sw

Across: (k), kw, (m), mw

This side: [k], [kw], s, sw

Across: m ,mw

This side: k, kw

Across: m, mw, (s), (sw)

This side: k, kw, [m], [mw]

Across: s, sw

This side: kw, mw

Across: (k), (m), s, sw

This side: kw, mw, [sw]

Across: k ,m, s

This side: sw

Across: k, (kw), m, (mw), s

This side: , sw

Across: k, kw, m, mw

Across: k, kw, m, mw, (s), (sw)

* Thanks to Karthik for notations

## 2 answers to this question

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This may have been posted before in this forum, and the solution I posted then had a slight violation.

It's an interesting puzzle because it takes only one move look ahead to find wrong moves.

Most moves are immediately dictated.

If two women cross, km [Rule 2] one will return, and there is no legal next crossing.
If a man crosses he must take his wife [Rule 3] Ss is one possibility, Kk [equivalently Mm] is the other.
Since S and s have travel restrictions [Rule 2] let's cross them together.

Ss cross S returns [s returning violates Rule 3]

Kk | __ Kk | __
Mm | __ Mm | __
__ | Ss S_ | _s

Now km may cross without one of them having to return:

km cross s returns

K_ | _k K_ | _k
M_ | _m M_ | _m
S_ | _s Ss | __

KM cross [Rule 2] and a couple must return [Rule 3]

KM cross Mm returns

__ | Kk __ | Kk
__ | Mm Mm | __
Ss | __ Ss | __

Two men must cross; but to obey Rule 2, Ss must be swapped with Kk.

Ss cross Kk returns

__ | Kk Kk | __
Mm | __ Mm | __
__ | Ss __ | Ss

Now you can cross two men.

KM cross s returns

_k | K_ _k | K_
_m | M_ _m | M_
__ | Ss _s | S_

Finally, mk cross S can return for his wife.

km cross S returns

__ | Kk __ | Kk
__ | Mm __ | Mm
_s | S_ Ss | __

Ss cross

__ | Kk
__ | Mm
__ | Ss
`The couples are Kk, Mm, Ss - uppercase are men.`

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This may have been posted before in this forum, and the solution I posted then had a slight violation.

It's an interesting puzzle because it takes only one move look ahead to find wrong moves.

Most moves are immediately dictated.

Yup, you got that right!

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