You have 5 chains with 3 links each. Cut a link and close it to connect two chains. How many number of links you need to cut to make a circular chain?

**Time to solve 10 minutes.**

**Hint:** Think logically, ask most important questions and find answers. The Five Chains With 3 Links Riddle is a challenging puzzle that will force you to think out-of-the-box.

### Solution to the Challenging Five Chains with 3 Links Riddle

#### Step 1: Analyze and Identify Your Real Task

As most of your friends would do, first cut a link and use it to join with a second link—a two link open chain you get. Continue this way, the conventional way, as most would do. You would find you need to cut 5 links. That can't be the solution, you realize. It is too easy. Anyone could have solved the puzzle then, and the puzzle won't have been a puzzle at all.

Your real task must then be to cut not 5, but 4 links.

#### Step 2: Why not solve a similar but simpler problem!

You may not know it, but this idea of solving a similar but simpler problem is a well-known problem solving technique used by many who need to solve different types of tricky problems, especially in research and development for new products, and in maths.

**Obvious simpler puzzle:** instead of 5 chain links, you decide to create a closed chain from 4 chains each with 3 links.

**Analyze the number of gaps:** Following a systematic path, place the four chains in a line side by side and count the number of gaps. After all, closing these 4 gaps is what you need to do for making a closed chain of 12 links.

As you have expected, to make a 12-link circular chain with 4 chain links, you need to close 4 gaps, just as you needed to cut 5 links to make a circular chain from 5 chain links.

You are sure now that somehow you have to reduce this number of 4 gaps to 3. This is the main challenge.

#### Step 3: Think in Logic Chain, Exploring Alternatives: Jump the Gap to the Inventive solution

Till now you were cutting one link each from one chain and failing. What is the other alternative! This is where you meet a gap in thinking that you need to jump across. We call this, inventive solution gap. Some can jump across this gap to reach the inventive solution instinctively. To me, instinctive inventive solution is uncertain. The sudden breakthrough brain-wave may or may not come at all.

Instead, I follow a technique to reach the inventive solution, the Property change analysis technique, a very powerful one, mainly used for inventive out-of-the-box thinking.

#### Step 4: Use Property change analysis inventive technique to make your 12-link closed chain

When solution to a problem seems impossible, use property change analysis technique. Its three steps are:

- Identify all properties of the most important thing, and
- Imagine the ways you can change each property. Imagine all the different ways.
- For a problem that seems unsolvable, you must have taken for granted one of the property changes. It never crossed your mind that you could change the particular property in a new, unorthodox way. It is a certainty. Otherwise, the problem will truly be unsolvable.

In this case, without hesitation you were opening one link from each chain. *Choosing a chain and cutting its link are the two actions or properties* of the **most important thing chain.**

But all chains are same. No variation possible. **Choice property is of no use.**

Think again, what more you were doing? You were opening one link from the chosen chain. **You ignored all along the possibility of opening more than one link** from a chain. This is the variation of the property of opening a link of the chosen chain. **This is the crucial idea.** Take one step more.

#### Step 5: Solution to the simpler problem of forming a 12-link closed chain from four 3-link chains

Open all three links of one chain, any one chain. You have reduced the number of gaps to close from 4 to 3 and you have in your hand 3 links to close these three gaps. The figure of the closed circular chain looks nice. You have solved the simpler problem.

#### Step 6: Solution to the Challenging Five Chains With 3 Links Riddle

As before, carry out gap analysis. Mentally place all five numbers of 3-link chains in a line side by side and count gaps. It is 5.

- Cut all three links from any 3-link chain.
- Use these three links to close the three gaps in the four 3-link chains—a 15-link open chain is formed.

You don't have any spare cut link with you as a free resource. You have to cut one of the end links of the 15-link open chain to close the fourth and final gap.

To get a 15-link closed chain from five 3-link chains you have to cut a minimum of 4 links. Here is your 15-link circular chain with 4 minimum number of cuts.

#### An Additional Challenge

Can you now solve the puzzle of forming a circular chain from six 3-link chains? Think about how many gaps you will have, and how many links you will need to cut to close those gaps. Try to spot a pattern between the number of chains and the number of cuts required.

**Hint: **Think back to how many cuts were needed when using four and five 3-link chains!

### Conclusion

This is an inventive puzzle that requires thinking beyond conventional methods, using the property change analysis technique to discover the solution.

Frequently used problem solving technique of **solving a similar but simpler problem** provided the first step to be taken without resorting to random attempts. But, the powerful **inventive property change analysis technique** made it possible to take the all important jump across unknown territory to reach the **inventive solution.**

### More puzzles to enjoy

From our large collection of interesting puzzles enjoy: * Maze puzzles*,

**Riddles**,

*,*

**Mathematical puzzles***,*

**Logic puzzles***,*

**Number lock puzzles***,*

**Missing number puzzles***,*

**River crossing puzzles***and*

**Ball weighing puzzles***.*

**Matchstick puzzles**You may also look at the full collection of puzzles at one place in the **Challenging brain teasers with solutions: Long list.**

*Enjoy puzzle solving while learning problem solving techniques.*