Update README.md

README.md

@@ -34,7 +34,7 @@ tokenizer = AutoTokenizer.from_pretrained(model_name)
 
 instruction = "Please reason step by step, and put your final answer within \\boxed{}."
 prompt = "The arithmetic mean of 7, 2, $x$ and 10 is 9. What is the value of $x$?"
-# prompt = "Let $S$ be the set of points $(a,b)$ with $0 \le a,$ $b \le 1$ such that the equation \[x^4 + ax^3 - bx^2 + ax + 1 = 0\] has at least one real root.  Determine the area of the graph of $S.$"
+#prompt = "What is the smallest positive perfect cube that can be written as the sum of three consecutive integers?"
 # prompt = "How many r's are in the word \"strawberry\""
 
 messages = [
@@ -51,7 +51,10 @@ model_inputs = tokenizer([text], return_tensors="pt").to(model.device)
 
 generated_ids = model.generate(
     **model_inputs,
-    max_new_tokens=16384
+    max_new_tokens=16384,
+    do_sample=True,
+    temperature=0.6,
+    top_p=0.95
 )
 generated_ids = [
     output_ids[len(input_ids):] for input_ids, output_ids in zip(model_inputs.input_ids, generated_ids)
@@ -67,6 +70,56 @@ print(f"\nThink Mode: {think_mode}")
 print(f"Number of tokens: {num_tokens}")
 ```
 
+## Case Study
+
+**User:**    
+```
+1+1=?
+```
+
+**Thinkless-1.5B:**  
+```
+<short>
+To solve the problem \(1 + 1\), we will follow a step-by-step approach:
+
+1. **Identify the numbers involved**: We have the numbers 1 and 1.
+2. **Understand the operation**: The operation we need to perform is addition.
+3. **Perform the addition**: When we add 1 and 1 together, we get 2.
+
+So, the final answer is \(\boxed{2}\).
+```
+
+**DeepSeek-R1:**   
+```
+Okay, so I need to figure out what 1 plus 1 equals. Let me start by thinking about basic addition. When you add two numbers together, you're combining their values. So if I have one apple and someone gives me another apple, how many apples do I have in total? That should be two apples.
+
+Wait, let me make sure I'm not missing something here. In the simplest terms, addition is taking two quantities and putting them together. So 1 plus 1 means combining a single unit with another single unit. If I use my fingers, holding up one finger on my left hand and one on my right, then when I put them together, I have two fingers up. That seems right.
+
+But maybe there's a trick to this question. Sometimes problems that look easy might have a different answer depending on the context. For example, in binary, 1 + 1 equals 10. But the question doesn't specify a number system, so I should assume it's in the decimal system, which is the default. So in decimal, 1 + 1 is definitely 2.
+
+Another way to check is by using the number line. Starting at 1, if I move one unit to the right, I land on 2. That confirms it. Or using basic arithmetic rules: the sum of 1 and 1 is the next number in the sequence after 1, which is 2.
+
+I guess there's no ambiguity here. Unless the question is trying to be philosophical or something, but mathematically, it's straightforward. So the answer should be 2.
+
+The sum of 1 and 1 is calculated as follows:
+
+1 + 1 = 2
+
+In decimal arithmetic, adding the numbers 1 and 1 results in the number 2.
+```
+
+---
+
+**User:**   
+```
+Define\n\\[p = \\sum_{k = 1}^\\infty \\frac{1}{k^2} \\quad \\text{and} \\quad q = \\sum_{k = 1}^\\infty \\frac{1}{k^3}.\\] Find a way to write\n\\[\\sum_{j = 1}^\\infty \\sum_{k = 1}^\\infty \\frac{1}{(j + k)^3}\\] in terms of $p$ and $q.
+```
+
+**Thinkless-1.5B:**  
+```
+
+```
+
 
 ## Citation
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