Logic Riddles

Question: You're in a unbreakable room. You only have scissors and a 2-feet long rope and logic. There's a small window, big enough only to put one item through. The rope nor the scissors doesn't fit into the window. How do you escape?

Question: If a mountain climber climbed up a mountain one day from midnight to midnight the next day and does the same thing the following day when coming down the mountain, would there be a time at which he was at the same position on the mountain both day?

Question: A grandfather has a broken grandfather clock that is off by a minute every hour (too fast). He figures out a way, while keeping it running at the same rate, to make the clock say the correct time twice a day.

How could he do this?

Question: You put me on a table and cut me, but you don't eat me.

What am I?

Question: In 1940, a correspondent proposed the following question:

A man's age at death was one twenty-ninth of the year of his birth. How old was he in 1900?