1. A body is discovered in a park in Chicago in the middle of summer. It has a fractured skull and many other broken bones, but the cause of death was hypothermia.
Solution: A poor peasant from somewhere in Europe desperately wants to come to the United States. Lacking money for airfare, he stows away in the landing gear compartment of a jet. He dies of hypothermia in mid-flight and falls out when the compartment opens as the plane makes its final approach.
2. A man is driving his car. He turns on the radio, listens for five minutes, turns around, goes home, and shoots his wife.
Solution: The radio program is one of those shows where they call up someone at random and ask them a question. The announcer states the name and town of the man's wife as the person he would call next. He does so, and a male voice answers. From this, he gathered his wife was having an affair.