diff --git a/3sum/ppxyn1.py b/3sum/ppxyn1.py
new file mode 100644
index 0000000000..8912e7fa36
--- /dev/null
+++ b/3sum/ppxyn1.py
@@ -0,0 +1,32 @@
+# idea: sorting + two pointer
+# The idea was straightforward, but remove the duplication logic was the tricky.
+
+class Solution:
+    def threeSum(self, nums: List[int]) -> List[List[int]]:
+        nums.sort()
+        n = len(nums)
+        answer = []
+
+        for i in range(n):
+            if i > 0 and  nums[i] == nums[i-1]:
+                continue
+
+            left, right = i+1, n-1
+
+            while left < right:
+                s = nums[i] + nums[left] + nums[right]
+                if s == 0:
+                    answer.append([nums[i], nums[left], nums[right]])
+                    while left < right and nums[left] == nums[left+1]:
+                        left += 1
+                    while left < right and nums[right] == nums[right-1]:
+                        right -= 1
+                    left += 1
+                    right -= 1
+                elif s < 0:
+                    left += 1
+                else:
+                    right -= 1
+        return answer
+
+
diff --git a/climbing-stairs/ppxyn1.py b/climbing-stairs/ppxyn1.py
new file mode 100644
index 0000000000..7515d102c4
--- /dev/null
+++ b/climbing-stairs/ppxyn1.py
@@ -0,0 +1,20 @@
+# idea: DP
+# I'm not always sure how to approach DP problems. I just try working through a few examples step by step and then check that it would be DP.
+# If you have any suggestions for how I can come up with DP, I would appreciate your comments :)
+
+class Solution:
+    def climbStairs(self, n: int) -> int:
+        if n <= 2:
+            return n
+        dp = [0] * (n+1)
+        dp[2], dp[3] = 2, 3
+        
+        #for i in range(4, n): error when n=4       
+        for i in range(4, n+1):
+            dp[i] = dp[i-1] + dp[i-2]
+        
+        return dp[n]
+    
+    
+
+
diff --git a/product-of-array-except-self/ppxyn1.py b/product-of-array-except-self/ppxyn1.py
new file mode 100644
index 0000000000..f5fb626756
--- /dev/null
+++ b/product-of-array-except-self/ppxyn1.py
@@ -0,0 +1,17 @@
+# idea: O(n) - There is no multiplication calculate it as O(1) / addition is possible
+
+class Solution:
+    def productExceptSelf(self, nums: List[int]) -> List[int]:
+        length = len(nums)
+        answer = [1] * length
+        
+        prefix,suffix = 1,1
+        for i in range(length):       
+            answer[i] = prefix
+            prefix *= nums[i]
+        for j in range(length - 1, -1, -1):  
+            answer[j] *= suffix
+            suffix *= nums[j]
+        return answer
+    
+
diff --git a/valid-anagram/ppxyn1.py b/valid-anagram/ppxyn1.py
new file mode 100644
index 0000000000..77ab26595a
--- /dev/null
+++ b/valid-anagram/ppxyn1.py
@@ -0,0 +1,27 @@
+#idea: dictionary
+from collections import Counter 
+
+class Solution:
+    def isAnagram(self, s: str, t: str) -> bool:
+        s_dic = Counter(sorted(s))
+        t_dic = Counter(sorted(t))
+        print(s_dic, t_dic)
+        return s_dic==t_dic
+
+
+
+# Trial and Error
+'''
+When you call sorted() on a dictionary, it only extracts and sorts the keys,and the values are completely ignored.
+class Solution:
+    def isAnagram(self, s: str, t: str) -> bool:
+        s_dic = Counter(s)
+        t_dic = Counter(t)
+        print(s_dic, t_dic)
+        return sorted(s_dic)==sorted(t_dic)
+'''
+
+
+
+
+
diff --git a/validate-binary-search-tree/ppxyn1.py b/validate-binary-search-tree/ppxyn1.py
new file mode 100644
index 0000000000..d91bc1346a
--- /dev/null
+++ b/validate-binary-search-tree/ppxyn1.py
@@ -0,0 +1,20 @@
+# idea: -
+# # Definition for a binary tree node.
+# class TreeNode:
+#     def __init__(self, val=0, left=None, right=None):
+#         self.val = val
+#         self.left = left
+#         self.right = right
+class Solution:
+    def isValidBST(self, root: Optional[TreeNode]) -> bool:
+        def dfs(node, low, high):
+            if not node:
+                return True
+            if not (low < node.val  < high):
+                return False
+            return dfs(node.left, low, node.val) and dfs(node.right, node.val, high)
+        return dfs(root, float('-inf'), float('inf'))
+    
+
+    
+