problem string | solution string | answer string | gemini_solution string | incorrect_solution string | rephrased_solution string | intervention dict | intervention_solution string | full_guidance string | full_guidance_prompt string | problem_id int64 |
|---|---|---|---|---|---|---|---|---|---|---|
You are a professional Sudoku puzzle solver. Please solve the following Sudoku variant.
## Format Explanation ##
Coordinates:
- We will use r{x}c{y} coordinates. For example, r1c1 is the top-left cell at row 1 column 1, r1c2 is the cell to the right at row 1 column 2, r2c1 is the cell below at row 2 column 1, and so o... |
<vl><value3><r5><c4><co><+><value2><r4><c5><co><+><value2><r6><c4><co><+><value2><r6><c6><co><+><value4><r4><c3><co><+><value4><r4><c4><co><+><value4><r4><c5><co><-><value2><r4><c5><co><+><value4><r4><c6><co><+><value4><r4><c7><cl><value0><r5><c4><co><-><value2><r6><c4><co><-><value2><r6><c6><co><+><value4><r3><c9><c... | 394867521561243879728195463217436958489571632653928147132659784975384216846712395 | Based on the provided rules, visual elements, and the reference solution logic, here is the step-by-step resolution of the Sudoku grid:
1. **Box 5 (Center):** The 11-cage covers the entire 3x3 box. To satisfy the Heyawake rules (shaded cells cannot touch) and the sum of 11, the box must have 5 shaded cells in a "dice... | We are given a **Sudoku variant** with **killer cages**, **shaded cells**, and **circles** indicating constraints.
Let’s carefully analyze and solve this step by step.
---
## 🔍 Understanding the Puzzle
### Rules Recap:
1. **Standard Sudoku rules** apply: each row, column, and 3×3 box contains digits 1–9 with no re... | Let's solve the Sudoku puzzle step-by-step, guided by the reference solution and the rules provided.
---
### **Understanding the Puzzle**
We are given:
- A **9x9 Sudoku grid** with all cells initially blank.
- Several **killer cages** (sum constraints), each with a value and a list of cells.
- **Circles** (white, bl... | {
"content": "Before proceeding with any further deductions, let's verify the cage constraints. For any group of cells with a sum value, the minimum possible sum of distinct digits (1 through 9) is 1+2+3+4 = 10 for 4 cells. Since the given cages have sum 3 for 4 cells, this is mathematically impossible. Therefore, th... | We are given a **Sudoku variant** with **killer cages**, **shaded cells**, and **circles** indicating constraints.
Let’s carefully analyze and solve this step by step.
---
## 🔍 Understanding the Puzzle
### Rules Recap:
1. **Standard Sudoku rules** apply: each row, column, and 3×3 box contains digits 1–9 with no re... | <Detailed Verification Log>
- Substep 29: The student correctly identifies the cage B (r1c4, r2c3, r2c4, r2c5) with sum 3 and four cells.
- Substep 30: The student correctly notes that the minimum sum of four distinct positive digits is 1+2+3+4 = 10.
- Substep 31: The student correctly identifies that 3 < 10, so the su... | <|im_start|>user
You are an expert Sudoku solver. You will be given a Sudoku problem and a reference solution to the problem. Your task is to solve the problem step-by-step guided by the reference solution.
# Problem #
You are a professional Sudoku puzzle solver. Please solve the following Sudoku variant.
## Format E... | 0 |
"You are a professional Sudoku puzzle solver. Please solve the following Sudoku variant.\n\n## Forma(...TRUNCATED) | " \n\nThat's unsurprising, right? I am going to just plunge in, give this a go, learn something abou(...TRUNCATED) | 865913427723648519419752638954327861136589274287461395672894153341275986598136742 | "Based on the rules and the reference solution provided, here is the step-by-step derivation of the (...TRUNCATED) | "We are given a complex Sudoku variant with multiple constraints:\n\n- Standard Sudoku rules: each r(...TRUNCATED) | "It appears that the reference solution provided is a highly disorganized, partially coherent, and i(...TRUNCATED) | {"content":"Do not assume that the light gray path (r9c4 r9c5 r9c6 r8c5 r7c4) requires increasing va(...TRUNCATED) | "We are given a complex Sudoku variant with multiple constraints:\n\n- Standard Sudoku rules: each r(...TRUNCATED) | "3 is odd → yes\n\n**Substep 469:** - sum = 8 → max = 4 → r9c2 + r9c3 = 5 → (1,4), (2,3), (3(...TRUNCATED) | "<|im_start|>user\nYou are an expert Sudoku solver. You will be given a Sudoku problem and a referen(...TRUNCATED) | 8 |
"You are a professional Sudoku puzzle solver. Please solve the following Sudoku variant.\n\n## Forma(...TRUNCATED) | " \n\nAnyway, I'm going to have a go now. Let's get cracking. \n\nSo the V in row 3, columns 3 and 4(...TRUNCATED) | 683572941942618735751493628475321896369845217218967354196734582534286179827159463 | "Based on the rules and the step-by-step logical deduction guided by the reference solution, here is(...TRUNCATED) | "We are given a Sudoku variant with additional constraints involving:\n\n- **Pumpkin (darkorange lin(...TRUNCATED) | "Let's solve this Sudoku puzzle step-by-step, guided by the visual elements and the reference soluti(...TRUNCATED) | {"content":"Before assigning values to r3c4 and r3c6, list all possible values of r3c5 (7,8,9) that (...TRUNCATED) | "We are given a Sudoku variant with additional constraints involving:\n\n- **Pumpkin (darkorange lin(...TRUNCATED) | "I apologize for the confusion and the incomplete analysis. After a thorough review, I recognize tha(...TRUNCATED) | "<|im_start|>user\nYou are an expert Sudoku solver. You will be given a Sudoku problem and a referen(...TRUNCATED) | 9 |
"You are a professional Sudoku puzzle solver. Please solve the following Sudoku variant.\n\n## Forma(...TRUNCATED) | " \n\ndigit I've done all the rules okay let's get let's have a go let's get cracking what can we do(...TRUNCATED) | 321564546321215436634152163245452613 | "To solve this Mini Golf Sudoku puzzle, we must place digits 1-6 in each row, column, and 2x3 box, w(...TRUNCATED) | "Let's solve this **6x6 Sudoku variant** step by step, carefully applying all the rules and visual c(...TRUNCATED) | "Let's solve this 6×6 Sudoku variant step by step, guided by the rules and visual elements provided(...TRUNCATED) | {"content":"The rule 'One of the four cells surrounding the circled 2 contains 2' must be interprete(...TRUNCATED) | "Let's solve this **6x6 Sudoku variant** step by step, carefully applying all the rules and visual c(...TRUNCATED) | " student made a critical error in the interpretation of the \"2\" rule.**\n\nThe student's attempt (...TRUNCATED) | "<|im_start|>user\nYou are an expert Sudoku solver. You will be given a Sudoku problem and a referen(...TRUNCATED) | 10 |
"You are a professional Sudoku puzzle solver. Please solve the following Sudoku variant.\n\n## Forma(...TRUNCATED) | " \n\nI'm going to start now. See how we go. Let's get cracking. So, we have... Well, I mean, normal(...TRUNCATED) | 316458729587293164249671853935847612864125397172936485728514936693782541451369278 | "The solution to the Sudoku puzzle is derived by carefully analyzing the constraints provided by the(...TRUNCATED) | "Let's solve this Sudoku variant step by step.\n\nWe are given:\n\n- A standard 9×9 Sudoku grid wit(...TRUNCATED) | "Let's solve the Sudoku puzzle step-by-step, guided by the reference solution and the provided visua(...TRUNCATED) | {"content":"Before making any assumptions about the arrow sum, verify the rule: does the sum of the (...TRUNCATED) | "Let's solve this Sudoku variant step by step.\n\nWe are given:\n\n- A standard 9×9 Sudoku grid wit(...TRUNCATED) | "9c2 + r9c3 + 9 + S + S + r9c9\n\n**Substep 329:** = r9c1 + r9c2 + r9c3 + 9 + 2S + r9c9\n\n**Substep(...TRUNCATED) | "<|im_start|>user\nYou are an expert Sudoku solver. You will be given a Sudoku problem and a referen(...TRUNCATED) | 11 |
"You are a professional Sudoku puzzle solver. Please solve the following Sudoku variant.\n\n## Forma(...TRUNCATED) | "\n\n<co><+><value6><r4><c4><cd><+><value2><r3><c4><co><+><value6><r3><c2><co><-><value6><r3><c2><co(...TRUNCATED) | 389576421675124938241398576134257689926481753857963142718635294562849317493712865 | "Based on the reference solution and the provided logs, here is the step-by-step derivation of the f(...TRUNCATED) | "Let's solve this Sudoku variant step by step, incorporating all the rules and visual elements.\n\n-(...TRUNCATED) | "Let's solve the Sudoku puzzle step-by-step, guided by the rules and visual elements provided.\n\n--(...TRUNCATED) | {"content":"Before proceeding with any deductions involving the 'v between r9c3 and r10c3' clue, ver(...TRUNCATED) | "Let's solve this Sudoku variant step by step, incorporating all the rules and visual elements.\n\n-(...TRUNCATED) | "I see that the student's attempt contains a critical error in the interpretation of the visual elem(...TRUNCATED) | "<|im_start|>user\nYou are an expert Sudoku solver. You will be given a Sudoku problem and a referen(...TRUNCATED) | 13 |
"You are a professional Sudoku puzzle solver. Please solve the following Sudoku variant.\n\n## Forma(...TRUNCATED) | " \n\nBut I'm going to start now. Let's get cracking. And with no numbers in the grid, but V's, I am(...TRUNCATED) | 794125863125863794863794125941258637258637941637941258412586379586379412379412586 | "Based on the rules and the step-by-step deduction guided by the reference solution, here is the sol(...TRUNCATED) | "We are given a complex Sudoku variant with additional constraints. Let's solve it step by step, car(...TRUNCATED) | "Let's solve this Sudoku puzzle step-by-step, guided by the rules and visual elements provided.\n\n-(...TRUNCATED) | {"content":"Re-examine the grey line constraint. The circles at r1c1 and r6c6 define the bounds. The(...TRUNCATED) | "We are given a complex Sudoku variant with additional constraints. Let's solve it step by step, car(...TRUNCATED) | " in (1,6) → values 2,3,4,5\n\n**Substep 279:** The diagonal values are 1,2,3,4,5,6 — so values (...TRUNCATED) | "<|im_start|>user\nYou are an expert Sudoku solver. You will be given a Sudoku problem and a referen(...TRUNCATED) | 16 |
"You are a professional Sudoku puzzle solver. Please solve the following Sudoku variant.\n\n## Forma(...TRUNCATED) | " \n\nYou've had a go. Let's get cracking. So, so we've got a 6, the 6 clue is smaller. Those two di(...TRUNCATED) | 512346436125164253325461251634643512 | "To solve this 6x6 Sudoku variant, we will use the provided rules and the reference solution to dedu(...TRUNCATED) | "It appears there is a misunderstanding or misalignment in the problem description. Let's carefully (...TRUNCATED) | "Let's carefully solve this 6×6 Sudoku variant step by step, guided by the reference solution and t(...TRUNCATED) | {"content":"Even though only two diagonal sums are given, the reference solution shows that addition(...TRUNCATED) | "It appears there is a misunderstanding or misalignment in the problem description. Let's carefully (...TRUNCATED) | "I see that the student's attempt contains a fundamental misunderstanding of the puzzle's structure (...TRUNCATED) | "<|im_start|>user\nYou are an expert Sudoku solver. You will be given a Sudoku problem and a referen(...TRUNCATED) | 18 |
"You are a professional Sudoku puzzle solver. Please solve the following Sudoku variant.\n\n## Forma(...TRUNCATED) | "\n\n<vl><value8><r7><c4><cl><value0><r7><c4><cd><+><value3><r4><c5> I'm going to restart the clock (...TRUNCATED) | 573168429816492753249735186681357942924681375357924618795246831138579264462813597 | "Based on the reference solution and the rules of the puzzle, here is the step-by-step derivation of(...TRUNCATED) | "We are given a Sudoku puzzle with a variant rule involving **yellow divisor lines**. Let's carefull(...TRUNCATED) | "Let's solve this Sudoku puzzle step-by-step, guided by the rules and the visual constraints provide(...TRUNCATED) | {"content":"Even though there are no initial numbers, the yellow lines provide constraints on which (...TRUNCATED) | "We are given a Sudoku puzzle with a variant rule involving **yellow divisor lines**. Let's carefull(...TRUNCATED) | "\n- 12: not in 1-9\n- 18: not in 1-9\n\n**Substep 229:** So M must be 6 or 8.\n\n**Substep 230:** S(...TRUNCATED) | "<|im_start|>user\nYou are an expert Sudoku solver. You will be given a Sudoku problem and a referen(...TRUNCATED) | 20 |
"You are a professional Sudoku puzzle solver. Please solve the following Sudoku variant.\n\n## Forma(...TRUNCATED) | " \n\num and see how you get on with unique sums by sammy piano i am going to restart my clock and s(...TRUNCATED) | 986713452324856197157294368248367915593182746671945283719528634862439571435671829 | "Based on the step-by-step analysis of the puzzle and the reference solution, here is the solution t(...TRUNCATED) | "We are given a **Sudoku variant** with **killer cages** and a **light gray square** (which contains(...TRUNCATED) | "Let's solve this Sudoku puzzle step-by-step, guided by the reference solution and logical deduction(...TRUNCATED) | {"content":"Before assuming any sum values for the cages, verify that the problem statement includes(...TRUNCATED) | "We are given a **Sudoku variant** with **killer cages** and a **light gray square** (which contains(...TRUNCATED) | "# Detailed Verification Log\n\n- **Substep 1:** The student correctly identifies the puzzle type (S(...TRUNCATED) | "<|im_start|>user\nYou are an expert Sudoku solver. You will be given a Sudoku problem and a referen(...TRUNCATED) | 21 |
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