Put the verbs in the brackets into the right form observing the rules of the sequence of tenses.
1. I was sure that he (come) in time. 2. Vadim wanted to know about the books which he (leave) here a day before. 3. I finally said that I (not + wish) to hear any more about the subject. 4. Mark remembered that he (leave) the notebook at the hotel. 5. We have heard that he (be) very clever. 6. My wife told me that in an hour she (go) for a walk. 7. The boy did not know that water (boil) at 100°. 8. He told us how he (live) in the North. We were quite astonished when he said that in the far North the sun never (rise) in winter and never (set) in summer. 9. Last year I skated much better than I (do) now. 10. The teacher told us that there (be) 26 letters in the English alphabet. 11. The pupil who (answer) questions now did not know any English last year. 12. One day the boy asked his father how long elephants (live). 13. My wife (seem) surprised to find us there. She (say) she (think) that we (start) hours ago. Then she (tell) me she (go) probably for a sail. 14. Poor uncle (rush) to the nursery to see what his young son (do) there as there (be) a terrible noise in the house. 15. They (begin) to ask me questions about myself and pretty soon they (have) my story. Finally they (tell) me I (answer) their purpose. I (say) I (be) sincerely glad, and (ask) what it (be). Then one of them (hand) me an envelope, and (say) I (find) the explanation inside.

Правильные формы глаголов:

1. I was sure that he would come in time.
   После глагола в прошедшем времени was sure будущее действие передаётся формой would + infinitive.

2. Vadim wanted to know about the books which he had left there a day before.
   Книги он оставил раньше, чем захотел узнать о них, поэтому нужен Past Perfect — had left.

3. I finally said that I did not wish to hear any more about the subject.
   Желание относилось к моменту высказывания в прошлом, поэтому did not wish.

4. Mark remembered that he had left the notebook at the hotel.
   Он оставил тетрадь до того, как вспомнил об этом: had left.

5. We have heard that he is very clever.
   Характеристика человека остаётся актуальной в настоящем, поэтому используется Present Simple — is.

6. My wife told me that in an hour she would go for a walk.
   Будущее действие по отношению к прошлому моменту: would go.

7. The boy did not know that water boils at 100°.
   Это общеизвестный факт, поэтому время не меняется: boils.

8. He told us how he lived in the North. We were quite astonished when he said that in the far North the sun never rises in winter and never sets in summer.
   Lived описывает его жизнь в прошлом. Закономерные природные явления выражаются в настоящем времени: rises, sets.

9. Last year I skated much better than I do now.
   Слово now указывает на настоящее время, поэтому: do.

10. The teacher told us that there are 26 letters in the English alphabet.
    Это постоянный факт, поэтому: are.

11. The pupil who is answering questions now did not know any English last year.
    Действие происходит сейчас: is answering.

12. One day the boy asked his father how long elephants live.
    Речь идёт об общем факте, поэтому: live.

13. My wife seemed surprised to find us there. She said she thought that we had started hours ago. Then she told me she would probably go for a sail.
    Thought относится к моменту, когда она это сказала; отправились мы раньше — had started. Будущее по отношению к прошлому: would go.

14. Poor uncle rushed to the nursery to see what his young son was doing there as there was a terrible noise in the house.
    Действие сына происходило в тот момент: was doing. Шум также был в доме в тот момент: was.

15. They began to ask me questions about myself and pretty soon they had my story. Finally they told me I had answered their purpose. I said I was sincerely glad, and asked what it was. Then one of them handed me an envelope, and said I would find the explanation inside.
    Здесь had означает «имели, получили» и является формой Past Simple. Had answered показывает действие, завершившееся до того, как они сообщили результат. После said используются формы was, was, would find по правилу согласования времён.