# # Exploring Candy Distribution: A Combinatorial Challenge

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## Chapter 1: The Candy Conundrum

What’s your favorite candy? For me, nothing satisfies my sweet cravings quite like a Hershey white chocolate bar! Today’s mathematical puzzle invites you to explore how to distribute 7 unique candies into 3 separate jars.

Here’s a little hint: whatever rule applies to the red jar is also applicable to the blue jar. Take a moment to pause, grab some paper and a pen, and give it a try. Once you’re ready, continue reading for the solution!

### Solution

If there were no restrictions on how many candies could go in each jar, each of the 7 candies could be placed into any of the 3 jars. Thus, we have:

3^7

In this scenario, we would arrive at a total of (3^7) ways to distribute the candies. However, this calculation includes instances where either the red or blue jar may end up empty.

## Addressing Empty Jars

Now, let’s consider the situation where either the red jar or the blue jar is empty.

If the red jar is not used, all 7 candies can only go into the blue and green jars. Thus, we have:

2^7

This scenario applies equally when the blue jar is empty, resulting in another (2^7) distribution.

Notice the illustration above depicts one possible way of distributing candies when the red jar must remain empty—meaning all candies are placed in the green jar. We've inadvertently counted this arrangement twice, so we need to subtract it from our total.

## Final Calculation

Thus, the total number of arrangements where either the red or blue jar is empty is:

2^7 + 2^7 - 1

By subtracting this from (3^7), we can find our final answer.

And that’s the solution! Fascinating, right? What were your thoughts while tackling this puzzle? I’d love to hear your insights in the comments below.

## Chapter 2: Conclusion

Feel free to share this list of engaging math puzzles available on Medium with your friends:

**Math Puzzles**

The best math puzzles on Medium, covering Algebra, Geometry, Calculus, Number Theory, and more!

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Happy Solving!

Bella