Everybody has to cross the river

So what's the problem? Only two people at a time. Doesn't say how many sons or daughters. Father takes son across, comes back for another son. Mother takes daughter across, comes back for another daughter. Policeman and thief cross together.

I still don't see the problem. This is childishly simple.

Why not?

Clearly they have bigger problems than just crossing a river.

But the father can't stay with the sons without the mother and the mother can't stay with the sons without the father.

Your solution doesn't account for that, unless the sons wait outside while the father takes them across one at a time.

So is it that there's only one son and one daughter?

I guess we have to assume that.

It says sons and daughters, plural. Obviously, the thief and the policeman have to be the last to cross, but that means someone gets left behind--whoever brought the raft back to that side of the river.

This is unsolvable. Do the math for yourself.

- Mother crosses with daughter 1, leaves her on the other side.
- Mother comes back alone.
- Mother crosses with daughter 2, leaves her on the other side.
- Mother comes back alone.
- Father crosses with wife, leaves her with the two daughters.
- Father comes back alone.
- Policeman crosses with thief.
- Mother comes back alone.
- Mother crosses with son 1, leaves him with the two sisters, policeman and thief.
- Mother comes back alone.
- Mother crosses with son 2, leaves him with brother, the two sisters, policeman and thief.
- Mother comes back alone.
- Mother and father cross together.

End of the trip.

If the mother and sons doesn't get along, how do you expect them to cross together on a raft that holds two, without the presence of father?
A better solution would be the following:
Policeman and thief cross. [F, M, S1, S2, D1, D2 ~~~ P, T]
Policeman crosses back (Golden opportunity to escape, and if the thief was I, I would). [F, M, S1, S2, D1, D2, P ~~~ T]
Policeman and a son 1 crosses. [F, M, S2, D1, D2 ~~~ P, S1, T]
Policeman and thief crosses back. [F, M, S2, D1, D2, P, T ~~~ S1]
father and son 2 crosses. [M, D1, D2, P, T ~~~ F, S2, S1]
Father crosses back. [F, M, D1, D2, P, T ~~~ S2, S1]
Father and mother crosses. [D1, D2, P, T ~~~ F, M, S2, S1]
Mother crosses back. [M, D1, D2, P, T ~~~ F, S2, S1]
Policeman and thief cross. [M, D1, D2 ~~~ F, S2, S1, P, T]
Father crosses back. [F, M, D1, D2 ~~~ S2, S1, P, T]
Mother and father cross. [D1, D2 ~~~ F, M, S2, S1, P, T]
Mother crosses back. [M, D1, D2 ~~~ F, S2, S1, P, T]
Mother and daughter 1 crosses. [D2 ~~~ F, S2, S1, P, T, M, D1]
Policeman and thief crosses back. [D2, P, T~~~ F, S2, S1, M, D1]
Policeman and daughter 2 crosses (Another golden opportunity to escape, and if the thief was I, I would). [T~~~ F, S2, S1, M, D1, D2, P]
Policeman crosses back. [P, T~~~ F, S2, S1, M, D1, D2]
Policeman and thief crosses. [~~~ F, S2, S1, M, D1, D2, P, T]

Obviously you are not reading the OP:





Leaving the thief with the family, contrary to the previous clause?

Again, where do you see me leave the thief with any of the family members, without the policeman?

As I understand it, the OP doesn't say the mother cannot cross with a son, he/she says: cannot stay.

here:

Back-pedaling, are you?

Playing on words, are you?

Having crossed the river, I'm looking for nicer horizons..

Why, to you, there seems to be nothing wrong with making assumptions to make the problem easier? And I suppose then, by such reasoning, we can assume that when individuals tour on the raft, they are not staying on the raft, but rather floating lightly as an ethereal personage where one of the regimen adumbrated by the clauses literally doesn't seem to hold.

Either the conditions are not well stated, or the problem is unsolvable. The mother cannot cross with a son, because then she would be on the raft with a son without the father present.

I'd say the expression of the conditions is flawed, or there is something not stated in the conditions. Furthermore, if there are sons and daughters (and the original statement is in the plural), it is unsolvable.

It's not unsolvable. Ice Demon solved it (plural version).

No, ID made assumptions which aren't covered in the stipulated conditions. Additionally, ID's solution leaves the father on the far bank with one of the daughters will the mother is on the nether bank.

By assumptions, if you mean limiting the number of sons and daughter to the number two, then two was chosen for simplicity's sake. The number of sons and daughters can be arbitrary, and all that requires to offset the numbers are just a repetition of two given steps in any one of the solutions possible. The basic idea of the solution remains unaltered, however.