Update README.md

README.md

@@ -1,46 +1,86 @@
 ---
 base_model: deepseek-ai/deepseek-math-7b-base
-license: apache-2.0
-pipeline_tag: text-generation
 tags:
 - alignment-handbook
 - generated_from_trainer
 widget:
-- example_title: Math problem
-  messages:
-  - role: user
-    content: For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$
-      have two distinct integer roots?
-  output:
-    text: "### Solution: \n1- For the polynomial \\\\( x^2 + kx + 36 \\\\) to have\
-      \ two distinct integer roots, let's denote these roots by \\\\( r_1 \\\\) and\
-      \ \\\\( r_2 \\\\).\n\n\n2- According to Vieta's formulas, the sum of the roots\
-      \ \\\\( r_1 + r_2 \\\\) is equal to \\\\(-k\\\\), and the product of the roots\
-      \ \\\\( r_1 \\\\cdot r_2 \\\\) is equal to 36.\n\n\n3- To find the distinct\
-      \ integer pairs \\\\((r_1, r_2)\\\\) whose product is 36, we need to determine\
-      \ all pairs of integers \\\\((r_1, r_2)\\\\) such that \\\\( r_1 \\\\cdot r_2\
-      \ = 36 \\\\) and \\\\( r_1 \\\\neq r_2 \\\\).\n\n\n4- From the equation \\\\\
-      ( r_1 + r_2 = -k \\\\), for each valid pair \\\\((r_1, r_2)\\\\), we can compute\
-      \ the corresponding value of \\\\( k \\\\).\n\n\n5- Finally, since we need the\
-      \ polynomial to have two distinct integer roots, we need to ensure that \\\\\
-      ( r_1 \\\\) and \\\\( r_2 \\\\) are distinct.\nLet's start by finding all pairs\
-      \ \\\\((r_1, r_2)\\\\) such that \\\\( r_1 \\\\cdot r_2 = 36 \\\\). We'll then\
-      \ determine the values of \\\\( k \\\\) and ensure the roots are distinct.\n\
-      ```python import itertools\n# Find all pairs (r1, r2) such that r1 * r2 = 36\
-      \ product_36 = 36 factor_pairs = []\nfor i in range(1, product_36 + 1):\n  if\
-      \ product_36 % i == 0:\n    pair = (i, product_36 // i)\n    if pair[0] != pair[1]:\
-      \ # Ensure distinct pairs\n      factor_pairs.append(pair)\n    \n    # Calculate\
-      \ k for each pair and ensure distinct integer roots\n    valid_k_values = set()\n\
-      \    for r1, r2 in factor_pairs:\n      if r1 != r2:\n        k = -(r1 + r2)\n\
-      \        valid_k_values.add(k)\n        \n    print((len(valid_k_values), sorted(valid_k_values)))\n\
-      \ ```\n \n ```output\n (4, [-37, -20, -15,-13])\n ```\n The distinct integer\
-      \ values of \\\\( k \\\\) that make the\npolynomial \\\\( x^2 + kx + 36 \\\\\
-      ) have two distinct integer roots are \\\\(-37, -20, -15, \\\\text{and} -13\\\
-      \\).\nTherefore, the number of such values of \\\\( k \\\\) is:\n[ \\\\boxed{4}\
-      \ \\\\]"
+  - example_title: Math problem
+    messages:
+      - role: user
+        content: >-
+          For how many values of the constant $k$ will the polynomial
+          $x^{2}+kx+36$ have two distinct integer roots?
+    output:
+      text: >-
+        ### Solution: 
+        
+        1- For the polynomial \\( x^2 + kx + 36 \\) to have two
+        distinct integer roots, let's denote these roots by \\( r_1 \\) and \\(
+        r_2 \\).
+
+
+
+        2- According to Vieta's formulas, the sum of the roots \\( r_1 + r_2 \\)
+        is equal to \\(-k\\), and the product of the roots \\( r_1 \\cdot r_2
+        \\) is equal to 36.
+
+
+
+        3- To find the distinct integer pairs \\((r_1, r_2)\\) whose product is
+        36, we need to determine all pairs of integers \\((r_1, r_2)\\) such
+        that \\( r_1 \\cdot r_2 = 36 \\) and \\( r_1 \\neq r_2 \\).
+
+
+
+        4- From the equation \\( r_1 + r_2 = -k \\), for each valid pair
+        \\((r_1, r_2)\\), we can compute the corresponding value of \\( k \\).
+
+
+
+        5- Finally, since we need the polynomial to have two distinct integer
+        roots, we need to ensure that \\( r_1 \\) and \\( r_2 \\) are distinct.
+
+        Let's start by finding all pairs \\((r_1, r_2)\\) such that \\( r_1
+        \\cdot r_2 = 36 \\). We'll then determine the values of \\( k \\) and
+        ensure the roots are distinct.
+
+        ```python import itertools
+
+        # Find all pairs (r1, r2) such that r1 * r2 = 36 product_36 = 36
+        factor_pairs = []
+
+        for i in range(1, product_36 + 1):
+          if product_36 % i == 0:
+            pair = (i, product_36 // i)
+            if pair[0] != pair[1]: # Ensure distinct pairs
+              factor_pairs.append(pair)
+            
+            # Calculate k for each pair and ensure distinct integer roots
+            valid_k_values = set()
+            for r1, r2 in factor_pairs:
+              if r1 != r2:
+                k = -(r1 + r2)
+                valid_k_values.add(k)
+                
+            print((len(valid_k_values), sorted(valid_k_values)))
+         ```
+         
+         ```output
+         (4, [-37, -20, -15,-13])
+         ```
+         The distinct integer values of \\( k \\) that make the
+        polynomial \\( x^2 + kx + 36 \\) have two distinct integer roots are
+        \\(-37, -20, -15, \\text{and} -13\\).
+
+        Therefore, the number of such values of \\( k \\) is:
+
+        [ \\boxed{4} \\]
+
+pipeline_tag: text-generation
 model-index:
 - name: NuminaMath-7B-TIR
   results: []
+license: apache-2.0
 ---
 
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