diff --git a/solution/2900-2999/2927.Distribute Candies Among Children III/README.md b/solution/2900-2999/2927.Distribute Candies Among Children III/README.md
new file mode 100644
index 0000000000000..a5ff2396e9b49
--- /dev/null
+++ b/solution/2900-2999/2927.Distribute Candies Among Children III/README.md
@@ -0,0 +1,167 @@
+# [2927. Distribute Candies Among Children III](https://leetcode.cn/problems/distribute-candies-among-children-iii)
+
+[English Version](/solution/2900-2999/2927.Distribute%20Candies%20Among%20Children%20III/README_EN.md)
+
+## 题目描述
+
+
+
+You are given two positive integers n and limit.
+
+Return the total number of ways to distribute n candies among 3 children such that no child gets more than limit candies.
+
+
+Example 1:
+
+
+Input: n = 5, limit = 2
+Output: 3
+Explanation: There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1).
+
+
+Example 2:
+
+
+Input: n = 3, limit = 3
+Output: 10
+Explanation: There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0).
+
+
+
+Constraints:
+
+
+ 1 <= n <= 1081 <= limit <= 108
+
+## 解法
+
+
+
+**方法一：组合数学 + 容斥原理**
+
+根据题目描述，我们需要将 $n$ 个糖果分给 $3$ 个小孩，每个小孩分到的糖果数在 $[0, limit]$ 之间。
+
+这实际上等价于把 $n$ 个球放入 $3$ 个盒子中。由于盒子可以为空，我们可以再增加 $3$ 个虚拟球，然后再利用隔板法，即一共有 $n + 3$ 个球，我们在其中 $n + 3 - 1$ 个位置插入 $2$ 个隔板，从而将实际的 $n$ 个球分成 $3$ 组，并且允许盒子为空，因此初始方案数为 $C_{n + 2}^2$。
+
+我们需要在这些方案中，排除掉存在盒子分到的小球数超过 $limit$ 的方案。考虑其中有一个盒子分到的小球数超过 $limit$，那么剩下的球（包括虚拟球）最多有 $n + 3 - (limit + 1) = n - limit + 2$ 个，位置数为 $n - limit + 1$，因此方案数为 $C_{n - limit + 1}^2$。由于存在 $3$ 个盒子，因此这样的方案数为 $3 \times C_{n - limit + 1}^2$。这样子算，我们会多排除掉同时存在两个盒子分到的小球数超过 $limit$ 的方案，因此我们需要再加上这样的方案数，即 $3 \times C_{n - 2 \times limit}^2$。
+
+时间复杂度 $O(1)$，空间复杂度 $O(1)$。
+
+
+
+### **Python3**
+
+
+
+```python
+class Solution:
+ def distributeCandies(self, n: int, limit: int) -> int:
+ if n > 3 * limit:
+ return 0
+ ans = comb(n + 2, 2)
+ if n > limit:
+ ans -= 3 * comb(n - limit + 1, 2)
+ if n - 2 >= 2 * limit:
+ ans += 3 * comb(n - 2 * limit, 2)
+ return ans
+```
+
+### **Java**
+
+
+
+```java
+class Solution {
+ public long distributeCandies(int n, int limit) {
+ if (n > 3 * limit) {
+ return 0;
+ }
+ long ans = comb2(n + 2);
+ if (n > limit) {
+ ans -= 3 * comb2(n - limit + 1);
+ }
+ if (n - 2 >= 2 * limit) {
+ ans += 3 * comb2(n - 2 * limit);
+ }
+ return ans;
+ }
+
+ private long comb2(int n) {
+ return 1L * n * (n - 1) / 2;
+ }
+}
+```
+
+### **C++**
+
+```cpp
+class Solution {
+public:
+ long long distributeCandies(int n, int limit) {
+ auto comb2 = [](int n) {
+ return 1LL * n * (n - 1) / 2;
+ };
+ if (n > 3 * limit) {
+ return 0;
+ }
+ long long ans = comb2(n + 2);
+ if (n > limit) {
+ ans -= 3 * comb2(n - limit + 1);
+ }
+ if (n - 2 >= 2 * limit) {
+ ans += 3 * comb2(n - 2 * limit);
+ }
+ return ans;
+ }
+};
+```
+
+### **Go**
+
+```go
+func distributeCandies(n int, limit int) int64 {
+ comb2 := func(n int) int {
+ return n * (n - 1) / 2
+ }
+ if n > 3*limit {
+ return 0
+ }
+ ans := comb2(n+2)
+ if n > limit {
+ ans -= 3 * comb2(n-limit+1)
+ }
+ if n-2 >= 2*limit {
+ ans += 3 * comb2(n-2*limit)
+ }
+ return int64(ans)
+}
+```
+
+### **TypeScript**
+
+```ts
+function distributeCandies(n: number, limit: number): number {
+ const comb2 = (n: number) => (n * (n - 1)) / 2;
+ if (n > 3 * limit) {
+ return 0;
+ }
+ let ans = comb2(n + 2);
+ if (n > limit) {
+ ans -= 3 * comb2(n - limit + 1);
+ }
+ if (n - 2 >= 2 * limit) {
+ ans += 3 * comb2(n - 2 * limit);
+ }
+ return ans;
+}
+```
+
+### **...**
+
+```
+
+```
+
+
diff --git a/solution/2900-2999/2927.Distribute Candies Among Children III/README_EN.md b/solution/2900-2999/2927.Distribute Candies Among Children III/README_EN.md
new file mode 100644
index 0000000000000..aa0b6dd2054ee
--- /dev/null
+++ b/solution/2900-2999/2927.Distribute Candies Among Children III/README_EN.md
@@ -0,0 +1,159 @@
+# [2927. Distribute Candies Among Children III](https://leetcode.com/problems/distribute-candies-among-children-iii)
+
+[中文文档](/solution/2900-2999/2927.Distribute%20Candies%20Among%20Children%20III/README.md)
+
+## Description
+
+You are given two positive integers n and limit.
+
+Return the total number of ways to distribute n candies among 3 children such that no child gets more than limit candies.
+
+
+Example 1:
+
+
+Input: n = 5, limit = 2
+Output: 3
+Explanation: There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1).
+
+
+Example 2:
+
+
+Input: n = 3, limit = 3
+Output: 10
+Explanation: There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0).
+
+
+
+Constraints:
+
+
+ 1 <= n <= 1081 <= limit <= 108
+
+## Solutions
+
+**Solution 1: Combinatorial Mathematics + Principle of Inclusion-Exclusion**
+
+According to the problem description, we need to distribute $n$ candies to $3$ children, with each child receiving between $[0, limit]$ candies.
+
+This is equivalent to placing $n$ balls into $3$ boxes. Since the boxes can be empty, we can add $3$ virtual balls, and then use the method of inserting partitions, i.e., there are a total of $n + 3$ balls, and we insert $2$ partitions among the $n + 3 - 1$ positions, thus dividing the actual $n$ balls into $3$ groups, and allowing the boxes to be empty. Therefore, the initial number of schemes is $C_{n + 2}^2$.
+
+We need to exclude the schemes where the number of balls in a box exceeds $limit$. Consider that there is a box where the number of balls exceeds $limit$, then the remaining balls (including virtual balls) have at most $n + 3 - (limit + 1) = n - limit + 2$, and the number of positions is $n - limit + 1$, so the number of schemes is $C_{n - limit + 1}^2$. Since there are $3$ boxes, the number of such schemes is $3 \times C_{n - limit + 1}^2$. In this way, we will exclude too many schemes where the number of balls in two boxes exceeds $limit$ at the same time, so we need to add the number of such schemes, i.e., $3 \times C_{n - 2 \times limit}^2$.
+
+The time complexity is $O(1)$, and the space complexity is $O(1)$.
+
+
+
+### **Python3**
+
+```python
+class Solution:
+ def distributeCandies(self, n: int, limit: int) -> int:
+ if n > 3 * limit:
+ return 0
+ ans = comb(n + 2, 2)
+ if n > limit:
+ ans -= 3 * comb(n - limit + 1, 2)
+ if n - 2 >= 2 * limit:
+ ans += 3 * comb(n - 2 * limit, 2)
+ return ans
+```
+
+### **Java**
+
+```java
+class Solution {
+ public long distributeCandies(int n, int limit) {
+ if (n > 3 * limit) {
+ return 0;
+ }
+ long ans = comb2(n + 2);
+ if (n > limit) {
+ ans -= 3 * comb2(n - limit + 1);
+ }
+ if (n - 2 >= 2 * limit) {
+ ans += 3 * comb2(n - 2 * limit);
+ }
+ return ans;
+ }
+
+ private long comb2(int n) {
+ return 1L * n * (n - 1) / 2;
+ }
+}
+```
+
+### **C++**
+
+```cpp
+class Solution {
+public:
+ long long distributeCandies(int n, int limit) {
+ auto comb2 = [](int n) {
+ return 1LL * n * (n - 1) / 2;
+ };
+ if (n > 3 * limit) {
+ return 0;
+ }
+ long long ans = comb2(n + 2);
+ if (n > limit) {
+ ans -= 3 * comb2(n - limit + 1);
+ }
+ if (n - 2 >= 2 * limit) {
+ ans += 3 * comb2(n - 2 * limit);
+ }
+ return ans;
+ }
+};
+```
+
+### **Go**
+
+```go
+func distributeCandies(n int, limit int) int64 {
+ comb2 := func(n int) int {
+ return n * (n - 1) / 2
+ }
+ if n > 3*limit {
+ return 0
+ }
+ ans := comb2(n+2)
+ if n > limit {
+ ans -= 3 * comb2(n-limit+1)
+ }
+ if n-2 >= 2*limit {
+ ans += 3 * comb2(n-2*limit)
+ }
+ return int64(ans)
+}
+```
+
+### **TypeScript**
+
+```ts
+function distributeCandies(n: number, limit: number): number {
+ const comb2 = (n: number) => (n * (n - 1)) / 2;
+ if (n > 3 * limit) {
+ return 0;
+ }
+ let ans = comb2(n + 2);
+ if (n > limit) {
+ ans -= 3 * comb2(n - limit + 1);
+ }
+ if (n - 2 >= 2 * limit) {
+ ans += 3 * comb2(n - 2 * limit);
+ }
+ return ans;
+}
+```
+
+### **...**
+
+```
+
+```
+
+
diff --git a/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.cpp b/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.cpp
new file mode 100644
index 0000000000000..008d72255bb8e
--- /dev/null
+++ b/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.cpp
@@ -0,0 +1,19 @@
+class Solution {
+public:
+ long long distributeCandies(int n, int limit) {
+ auto comb2 = [](int n) {
+ return 1LL * n * (n - 1) / 2;
+ };
+ if (n > 3 * limit) {
+ return 0;
+ }
+ long long ans = comb2(n + 2);
+ if (n > limit) {
+ ans -= 3 * comb2(n - limit + 1);
+ }
+ if (n - 2 >= 2 * limit) {
+ ans += 3 * comb2(n - 2 * limit);
+ }
+ return ans;
+ }
+};
\ No newline at end of file
diff --git a/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.go b/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.go
new file mode 100644
index 0000000000000..7705fb2057848
--- /dev/null
+++ b/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.go
@@ -0,0 +1,16 @@
+func distributeCandies(n int, limit int) int64 {
+ comb2 := func(n int) int {
+ return n * (n - 1) / 2
+ }
+ if n > 3*limit {
+ return 0
+ }
+ ans := comb2(n+2)
+ if n > limit {
+ ans -= 3 * comb2(n-limit+1)
+ }
+ if n-2 >= 2*limit {
+ ans += 3 * comb2(n-2*limit)
+ }
+ return int64(ans)
+}
\ No newline at end of file
diff --git a/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.java b/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.java
new file mode 100644
index 0000000000000..68684d6c5f5b5
--- /dev/null
+++ b/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.java
@@ -0,0 +1,19 @@
+class Solution {
+ public long distributeCandies(int n, int limit) {
+ if (n > 3 * limit) {
+ return 0;
+ }
+ long ans = comb2(n + 2);
+ if (n > limit) {
+ ans -= 3 * comb2(n - limit + 1);
+ }
+ if (n - 2 >= 2 * limit) {
+ ans += 3 * comb2(n - 2 * limit);
+ }
+ return ans;
+ }
+
+ private long comb2(int n) {
+ return 1L * n * (n - 1) / 2;
+ }
+}
\ No newline at end of file
diff --git a/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.py b/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.py
new file mode 100644
index 0000000000000..f08cfa1c4f041
--- /dev/null
+++ b/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.py
@@ -0,0 +1,10 @@
+class Solution:
+ def distributeCandies(self, n: int, limit: int) -> int:
+ if n > 3 * limit:
+ return 0
+ ans = comb(n + 2, 2)
+ if n > limit:
+ ans -= 3 * comb(n - limit + 1, 2)
+ if n - 2 >= 2 * limit:
+ ans += 3 * comb(n - 2 * limit, 2)
+ return ans
diff --git a/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.ts b/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.ts
new file mode 100644
index 0000000000000..39744f07459a0
--- /dev/null
+++ b/solution/2900-2999/2927.Distribute Candies Among Children III/Solution.ts
@@ -0,0 +1,14 @@
+function distributeCandies(n: number, limit: number): number {
+ const comb2 = (n: number) => (n * (n - 1)) / 2;
+ if (n > 3 * limit) {
+ return 0;
+ }
+ let ans = comb2(n + 2);
+ if (n > limit) {
+ ans -= 3 * comb2(n - limit + 1);
+ }
+ if (n - 2 >= 2 * limit) {
+ ans += 3 * comb2(n - 2 * limit);
+ }
+ return ans;
+}
diff --git a/solution/README.md b/solution/README.md
index d0bad30aff481..8a749e67a2299 100644
--- a/solution/README.md
+++ b/solution/README.md
@@ -2937,6 +2937,7 @@
| 2924 | [找到冠军 II](/solution/2900-2999/2924.Find%20Champion%20II/README.md) | | 中等 | 第 370 场周赛 |
| 2925 | [在树上执行操作以后得到的最大分数](/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/README.md) | | 中等 | 第 370 场周赛 |
| 2926 | [平衡子序列的最大和](/solution/2900-2999/2926.Maximum%20Balanced%20Subsequence%20Sum/README.md) | | 困难 | 第 370 场周赛 |
+| 2927 | [Distribute Candies Among Children III](/solution/2900-2999/2927.Distribute%20Candies%20Among%20Children%20III/README.md) | | 困难 | 🔒 |
## 版权
diff --git a/solution/README_EN.md b/solution/README_EN.md
index f0ff03da0eabd..8f0ba402e5b2b 100644
--- a/solution/README_EN.md
+++ b/solution/README_EN.md
@@ -2935,6 +2935,7 @@ Press Control + F(or Command + F on
| 2924 | [Find Champion II](/solution/2900-2999/2924.Find%20Champion%20II/README_EN.md) | | Medium | Weekly Contest 370 |
| 2925 | [Maximum Score After Applying Operations on a Tree](/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/README_EN.md) | | Medium | Weekly Contest 370 |
| 2926 | [Maximum Balanced Subsequence Sum](/solution/2900-2999/2926.Maximum%20Balanced%20Subsequence%20Sum/README_EN.md) | | Hard | Weekly Contest 370 |
+| 2927 | [Distribute Candies Among Children III](/solution/2900-2999/2927.Distribute%20Candies%20Among%20Children%20III/README_EN.md) | | Hard | 🔒 |
## Copyright
diff --git a/solution/summary.md b/solution/summary.md
index 6bb53362a86e9..e83950ae7d33e 100644
--- a/solution/summary.md
+++ b/solution/summary.md
@@ -2984,3 +2984,4 @@
- [2924.找到冠军 II](/solution/2900-2999/2924.Find%20Champion%20II/README.md)
- [2925.在树上执行操作以后得到的最大分数](/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/README.md)
- [2926.平衡子序列的最大和](/solution/2900-2999/2926.Maximum%20Balanced%20Subsequence%20Sum/README.md)
+ - [2927.Distribute Candies Among Children III](/solution/2900-2999/2927.Distribute%20Candies%20Among%20Children%20III/README.md)
diff --git a/solution/summary_en.md b/solution/summary_en.md
index a71aa30f7215c..d07b738f89598 100644
--- a/solution/summary_en.md
+++ b/solution/summary_en.md
@@ -2984,3 +2984,4 @@
- [2924.Find Champion II](/solution/2900-2999/2924.Find%20Champion%20II/README_EN.md)
- [2925.Maximum Score After Applying Operations on a Tree](/solution/2900-2999/2925.Maximum%20Score%20After%20Applying%20Operations%20on%20a%20Tree/README_EN.md)
- [2926.Maximum Balanced Subsequence Sum](/solution/2900-2999/2926.Maximum%20Balanced%20Subsequence%20Sum/README_EN.md)
+ - [2927.Distribute Candies Among Children III](/solution/2900-2999/2927.Distribute%20Candies%20Among%20Children%20III/README_EN.md)