This week’s Puzzle Corner activity is an adaptation of a classic puzzle from recreational mathematics. It is traditionally posed as a thought problem to be worked out in your head; as such, it is moderately difficult. However, I have found that many elementary school children can solve this puzzle -if they have manipulatives to make it concrete.
Most traditional versions of this puzzle show a picture of four separate pieces of chain, each with three links. The reader is challenged to find a way to join the four pieces into a circle by opening and closing only three links. Although this might seem impossible at first glance, persistent puzzle solvers are usually able to find a solution.
While the above thought problem is too difficult for many elementary students, they can often solve it if they are given plastic or metal snap rings (I used binder rings purchased in a stationary store) with which to model the problem. Since I rarely have a large enough supply of snap rings to do the puzzle as whole-class activity, I usually set it up at a center. I explain the challenge to the entire class on Monday and then let students go to the center at various times during the week. I usually set up two sets of rings so that more than one student can be at the center at a time. I ask students who have successfully solved the puzzle not to give the answer to others. On Friday, I let those who have solved the puzzle share their problem-solving processes with others in the class in a whole-class session.
Your mother has four separate pieces of gold chain, each with three links, that she wants to have made into a bracelet. The jeweler charges $10 for each link she has to open and solder closed. What is the minimum amount it will cost to have the bracelet made?
Hint: Use 12 snap rings to model the problem.
Click the arrow below to view the solution.
In It’s A Snap students were asked to find the minimum cost of making a necklace out of four sections of chain, each with three links, if it cost $10 to open and solder each link.
While the answer might seem to be $40 at first glance, the necklace can actually be made for $30. This is done by opening all three links in one of the sections and using each link to connect two of the remaining sections of chain. This way the necklace can be made by opening and soldering only three links.