Imagine you’re at a birthday party with a bunch of kids lined up excitedly, and you’re in charge of handing out candies. But here’s the twist—you’ve got to be fair about it based on their ratings. Let’s say each kid has a rating based on their behavior or performance, and you want to ensure everyone feels special on this day.
Here’s the catch: every child needs at least one candy, and you have to distribute the candies in such a way that if one child has a higher rating than their neighbor, they should get more candies than that neighbor. For example, if Timmy has a rating of 5 and Lucy next to him has a rating of 3, then Timmy can’t get less than Lucy. But if they have the same rating, they can get the same number of candies.
Picture this scenario: you’ve got 7 children, and their ratings are as follows:
– Child 1: 1
– Child 2: 0
– Child 3: 2
– Child 4: 0
– Child 5: 3
– Child 6: 0
– Child 7: 4
For simplicity, let’s say you decide to distribute candies based on their ratings while sticking to the rules mentioned above. What’s the minimum number of candies you would need to give out to satisfy these conditions?
Try to figure it out! Remember, you can’t give any kid less than one candy, and you must ensure that no child with a higher rating has fewer candies than their neighbors. You might find yourself doing a bit of juggling to get to the right answer. So, take a moment to crunch some numbers and come up with the magic number of candies to make this party a success! How many candies will it take in total to make sure everyone is happy and feels treated fairly?
Candy Distribution for Kids
Okay, so here’s the deal. We have 7 kids with the following ratings:
Every kid needs at least 1 candy, and we need to follow the rule where a kid with a higher rating than their neighbor gets more candies. Let’s start distributing!
Step 1: Initial Candy Distribution
First off, I’ll give everyone 1 candy. That’s the minimum:
Total candies so far: 7 candies.
Step 2: Adjusting Based on Ratings
Now, let’s make adjustments. We’ll go from left to right:
Final Candy Count
After all adjustments, here’s the candy distribution:
Now, let’s add ’em up:
Total candies = 1 + 1 + 2 + 1 + 3 + 1 + 4 = 13 candies.
Conclusion
So, to make sure every kid feels special and happy, we need a total of 13 candies!
To ensure a fair distribution of candies among the children based on their ratings, we have to follow a systematic approach. Each child must receive at least one candy, and those with higher ratings than their neighbors must receive more candies. Let’s first assign an initial count of one candy to each child. After this initial distribution, we will adjust the candies based on their ratings. Starting with the ratings given: Child 1: 1, Child 2: 0, Child 3: 2, Child 4: 0, Child 5: 3, Child 6: 0, Child 7: 4, the initial distribution appears as follows: [1, 1, 1, 1, 1, 1, 1].
Now, we must iterate through the list to correctly allocate candies. Moving left to right, if a child’s rating is higher than the previous child, they will receive one more candy than that child. When we apply this logic, we adjust as follows: Child 1 (1 candy), Child 2 (1 candy), Child 3 (2 candies), Child 4 (1 candy), Child 5 (3 candies), Child 6 (1 candy), Child 7 (4 candies). The distribution becomes: [1, 1, 2, 1, 3, 1, 4]. On inspection, we see that the total candies distributed amount to 1+1+2+1+3+1+4 = 13. Therefore, the minimum number of candies required to fairly distribute while adhering to the outlined ratings is 13.