Thirteen Diamonds

first weighing, go to III. If the scale tilts the opposite way it did at the first weighing, go to IV.
     
II.          The oddball is A3, A4 or B4. For the third weighing, weigh A3 against A4. If they balance, the oddball is B4. If they don’t balance, the oddball is the ball on the side of the scale tilted in the same direction (up or down) Group A was tilted at the first weighing.
     
III.     The oddball is A1 or B1. For the third weighing, weigh A1 against C1. If they balance the oddball is B1. If they don’t balance, it is A1.
     
IV.          The oddball is A2, B2 or B3. For the third weighing, weigh B2 against B3. If they balance, the oddball is A2. If they don’t balance, the oddball is the ball on the side of the scale tilted in the same direction (up or down) Group B was tilted at the first weighing.
     
V.               The oddball is in Group C. Set up a second weighing. On one side of the scale place the following balls: C1 and C2. On the other side of the scale place C3 and A1. If this weighing is in balance, go to VI. If it is not in balance, go to VII.
     
VI.          The oddball is C4. For the third weighing to determine whether it is heavier or lighter than the others, weigh C4 against any other ball.
     
VII.     The oddball is C1, C2 or C3. For the third weighing, weigh C1 against C2. If they balance, the oddball is C3. If they don’t balance, the oddball is the ball on the side of the scale tilted in the same direction (up or down) that ball’s side was tilted at the second weighing.
     
SOLUTION TO THE SEVEN BRIDGES PUZZLE
 
Given: The city of Bridgeton has a river running through it with two islands. One island has four bridges connecting to the mainland, two on each side. The other island has two bridges connecting to the mainland, one on each side. A seventh bridge connects the two islands. Is it possible, starting from any point you choose, to walk across all seven bridges without crossing one twice?
 
Solution: Draw a line to show the route you would take to cross all seven bridges. Note that this route has four places where exactly three paths intersect that you would have to take in order to cross all seven bridges. The general rule is: Count the number of intersections where an odd number of paths (or lines) come together and divide by two. That is the minimum number of walks you would have to take to cross all seven bridges without re-crossing any.
So the answer is no. You cannot cross all seven bridges without crossing one twice. If any one of the seven bridges were removed, you could cross the six remaining bridges without re-crossing any by starting at one of the intersections where an odd number of paths come together.

ABOUT THE AUTHOR
     
    After spending more than a quarter of a century as a pioneer in the computer industry, Alan Cook is well into his second career as a writer.
    Run into Trouble is about a footrace along the California coast in 1969 during the Cold War. But is the Cold War about to heat up? Drake and Melody, who worked undercover together in former lives, need to find the answer before all hell breaks loose.
    The Hayloft: a 1950s mystery and prize-winning Honeymoon for Three  feature Gary Blanchard, first as a high school senior who has to solve the murder of his cousin, and ten years later as a bridegroom who gets more than he bargained for on his honeymoon.
    Hotline to Murder takes place at a crisis hotline in Bonita Beach, California. When a listener is murdered, Tony and Shahla team up to uncover the strange worlds of their callers and find the killer.
    His Lillian Morgan mysteries, Catch a Falling Knife and Thirteen Diamonds , explore the secrets of retirement communities. Lillian, a retired mathematics professor from North Carolina, is smart, opinionated, and loves to solve puzzles, even when they involve murder.
    Alan splits his time between writing and walking, another passion. His inspirational, prize-winning book, Walking the World: Memories and Adventures , has information and adventure in equal parts. He is also the author of Walking to Denver , a light-hearted, fictional account of a walk he did.
    Freedom’s Light: Quotations from History’s Champions of Freedom , contains quotations from some of our favorite historical figures about personal freedom. The Saga of Bill the Hermit is a narrative poem about a hermit who decides that the single life isn’t all it’s cracked up to be.
    Alan lives