April 2011
Problem of the Month

Book Problem

Thirteen books -- three red (R), four orange (O), one yellow (Y), three green (G), and two blue (B) -- are positioned side by side on a bookshelf.   The positions are numbered consecutively 1 to 13.   Also:

(1) The four orange books are evenly spaced two positions apart, and their four positions total 36.

(2) The blue books have three books between them.

(3) Exactly two red books are next to each other.   Neither is at an end.

(4) The yellow book is the only book between an orange and a green book.

(5) One red book and one green book are at either end.

What is the order of the books?

Solution to the Problem:

G R R G Y O B O G O B O R

Begin with the Orange books: There are seven possibilities but only one adds up to 36:

So the orange books must be in positions 6, 8, 10, and 12 (whose sum is 36).

Since the yellow book is the only one between an orange and a green book, a green book must be at position 4 and the yellow book must be in position 5.

From statement (3), two red books must be in positions 2 and 3.

From statement (5), a green book must be in #1 and a red book must be in #13.

From statement (2), the blue books must be in positions 7 and 11, leaving the last green book in position #9.

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Trey Briggs	Mountain View High School, Mountain View, Wyoming
3. Adam Niemi	Mountain View High School, Mountain View, Wyoming
4. Mike Christy	Manhasset, New York
5. Mitchel Anderson	Mountain View High School, Mountain View, Wyoming
6. David and Judy Dixon	Bennettsville, South Carolina

Send any comments or questions to: David Pleacher