Answer: 10. Example: first, all 1000 wives move quietly, then one returns and 10 sheikhs leave. Finally, another returns and picks up the first. Evaluation: let the number of places not exceed 9. Consider the moment when the first sheikh appears on the other shore - or several at once, but not all, for they could not have crossed all at once. Then, together with them, their harems are also there, and with the remaining sheikhs, their harems are there. But then for the return trip, there is only one option: all the sheikhs present on the second shore return immediately, and they accumulate again on the first shore. Thus, all the sheikhs will never leave from there.
4. On the bank of the river stand 10 sheikhs, each with a harem of 100 wives. Also at the bank stands an $n$-person yacht. By law, a woman should not be on the same bank, on the yacht, or even at a transfer point with a man if her husband is not present. What is the smallest $n$ for which all the sheikhs and their wives can cross to the other bank without breaking the law?