In a candy store, there are four different flavors of candies: 6 strawberry, 8 chocolate, 7 mint, and 5 caramel. Lisa is selecting candies from a jar without looking. What is the minimum number of candies Lisa must select to guarantee that she has at least four candies of the same flavor?

To solve this problem, we can use the **pigeonhole principle**. The pigeonhole principle states that if you place more objects (candies in this case) into fewer containers (flavors) than the number of containers, at least one container must contain more than one object.

### Step-by-step explanation:

There are four different flavors of candies:
- 6 strawberry
- 8 chocolate
- 7 mint
- 5 caramel

Lisa needs to select enough candies to guarantee she gets **at least four candies of the same flavor**.

#### Worst-case scenario:
To find the minimum number of candies Lisa must select, we consider the worst-case scenario, where she picks candies in such a way that she avoids getting four candies of the same flavor as long as possible. 

In the worst case, she could pick:
- 3 strawberry
- 3 chocolate
- 3 mint
- 3 caramel

At this point, she would have selected 3 candies from each flavor, but she still does not have 4 candies of any single flavor. This totals to:

\[
3 + 3 + 3 + 3 = 12 \text{ candies}
\]

#### Next candy:
The next candy Lisa selects (the 13th candy) must be from one of the four flavors, which means that she will now have **4 candies of that flavor**. 

Thus, to guarantee that Lisa has at least 4 candies of the same flavor, she must select a minimum of **13 candies**.

### Final answer:
Lisa must select at least **13 candies** to guarantee she has at least four candies of the same flavor.

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Would you like more details or have any questions about this explanation? 

Here are some related questions to explore:

1. What if Lisa wanted at least 3 candies of the same flavor? How many should she select?
2. How does the pigeonhole principle apply in other real-life scenarios?
3. If there were 5 different flavors of candies, how would the minimum selection change?
4. What if the number of candies in each flavor was unequal, like 10 chocolate and 3 mint?
5. How would the situation change if Lisa could look at the candies while selecting?

**Tip:** The pigeonhole principle is a handy tool for solving problems where you need to ensure a certain number of items in a category, even when you don't know their exact distribution!

Learn how to solve a problem using the pigeonhole principle to determine the minimum number of candies Lisa must select to guarantee 4 of the same flavor. This problem involves 6 strawberry, 8 chocolate, 7 mint, and 5 caramel candies. Suitable for students in Grades 6-8.

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