IIM Interview Puzzle: How Many Ways Can You Distribute 6 Candies Fairly?

Question - You have 6 identical candies. You must distribute them among 3 persons — A, B, and C — such that:

Each individual can get at least 0, and at most 2 candies.
The candies are not distinct, and the individuals are distinct.
Then how many ways can you fairly count the distributions?

Let's count how many solutions solve the equation x + y + z = 6, under the restriction that no value is larger than 2.

Step 1: List all possible combinations under x, y, z ∈ {0, 1, 2} adding up to 6.

Let’s list out all the integer combinations of 3 variables (x, y, z) such that:

x + y + z = 6

Each variable is ≤ 2

Let’s go brute-force:

All possible triplets that satisfy these are:

(2, 2, 2)

That’s it.
Any other possible combination where someone gets more than 2 is not valid, and any less will add up to less than 6.

Final Answer = 1!
So, there is only one combination for this puzzle of (2, 2, 2) where each of the 3 people get 2 candies.

Puzzles, such as these, may look like trivial math problems, but they serve a greater purpose in an IIM interview: evaluating your ability to think logically within certain constraints, communicate your thinking clearly, and systematically approach a problem.

The final point to note? You should not be concerned about speed. You should show clarity, structure, and confidence in your thinking.

So, when you get a puzzle in an interview, remember: You are not just solving a puzzle; you are showing the way your mind works. And that may be the hook used to remember you.

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