Amy, Chris, Susan and Penny all live in different houses on Main Street. By a curious coincidence, the age of each woman is either seven years greater or seven years less than the number of her house. All of them are over 15 years old and less than 90; their ages are all different.
Amy said that the number of Chris’s house was even, and Chris remarked that the number of her house was greater that that of Penny’s. “My age,” she added proudly, “is a perfect cube.”
Susan said that the number of her house was greater by 3 than that of Amy’s, and that Penny’s age was an exact multiple of Amy’s age.
Penny, who has an unfortunate habit of complicating things, said that Chris’s age was either 27 or an even number other than 64. “Furthermore,” she commented, “Susan does not live at number 19.”
These remarks were unfortunately not all true. It was interesting to note that all remarks made by anyone who lived in an even-numbered house were false, and all remarks made by anyone who lived in an odd-numbered house were true.
What are their ages and the numbers of their houses?
Amy is 23 and lives in house number 16.
Chris is 64 and lives in house number 71.
Susan is 26 and lives in house number 19.
Penny is 69 and lives in house number 62.