Make a circular chain using four chain links, as in the figure. You can open and close maximum three links.
Time to solve: 10 minutes.
Hint: Think lateral.
Solution to Make a circular chain riddle: by common sense reasoning
First step is to make a quick trial to solve the puzzle. Look at the four chain links.
Start by opening an end link of chain 1 and close the link to an end link of chain 2. Chains 1 and 2 joined. In the same way, join chain links 3 and 4 by opening and closing and end link of chain 3 to an end link of chain 4. Two moves are used up. A pair of six link chains formed.
To join these two six link chains, one more link to open and close. That makes it the third link opening and closing. Result is a linear chain with 12 links, and not a circular chain. To make a circular chain from the 12 link linear chain, one more link to be opened and closed.
This is not the solution.
The trial made it clear how not to join the chains. All four chains being similar, the trial represents a general case.
Any possible unorthodox move of opening and closing a link?
We can choose the middle link of chain 1 for opening, but that will create a free standing added link. Not a way to the solution.
This seems to be a deadlock. Does it mean we cannot solve the riddle!
Property change analysis technique provides breakthrough
When solution to a problem seems impossible, use property change analysis technique,
- Identify all properties of the dominant entity, and
- Imagine the ways we can change each property. Imagine all the different ways.
For a problem that seems unsolvable, you must have taken for granted changes of one of the properties. It never crossed your mind that you could change the particular property in a new, unorthodox way.
The dominant entity here is the link chosen for opening and closing. We chose end links of the chains with no positive result.
What are the properties of a link chosen for opening and closing?
The link may be an end link or a middle link of a chain. In the experiment, always an end link chosen. We cannot choose the middle link because it will increase the unlinked parts of the chain.
This property represents position of the link in chosen chain. We cannot imagine any new unorthodox change in this property. This cannot be manipulated to solve the puzzle.
So two properties on choices to analyze:
- Choice of chain, and,
- Choice of link from chosen chain.
We can do nothing much about choosing a particular link of a chosen chain.
Consider now the choice of chain. We chose one link from each of three chains. Three links chosen from three chosen chains.
Taken-for-granted assumption is: We can choose a link only from each of three chains.
Any change in this property possible? Any unorthodox way to choose a chain?
What about opening all three links of ONLY ONE CHAIN?
Three original chains and three opened links. Unorthodox way to the solution discovered.
Solution: Use two of the three opened links to join the three original chains into an ELEVEN LINK linear chain. With the last open link, join the two ends of the eleven link linear chain to make it a circular chain of twelve links.
Lateral and intuitive thinking could also have solved the riddle, but both are uncertain brain actions.
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