Quandaries and Queries


Jo announces: I have no more than 999 books.
Jean says: No Jo, You have fewer than 1,000 books.
Mary says: Jo has at least 1 book.

Only one of these statements is true, How many books does Jo own?

I do not know HOW to approach this problem and solve it.

This is a college level math question.



Hi Debra,

I would do it by "intellegent" guess-and-check. The numbers in the problem are 1, 999 and 1000. Try these numbers and maybe others that are close.

Suppose Jo has exactly 1 book:

Jo's statement is true, She doesn't have more that 99 books.

Jean's statement is true, Jo has fewer than 1,000 books.

Mary's statement is also true but you don't need to even consider it since already more than one statement is true and thus Jo does not have 1 book.

Notice that the same argument is valid if Jo has 2 books, 3 books,... anything less than 999 books.
Suppose Jo has exactly 999 books: Who's statements are true? Suppose Jo has exactly 1000 books: Who's statements are true? Suppose Jo has exactly 1001 books: Who's statements are true?


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