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High-Degree Polynomial Factorization
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24-Point Game Generator and Solver
Generate Puzzle
Current Puzzle
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Generate New Puzzle
Difficulty Settings
Easy (Mostly Large Numbers)
Medium (Mixed Numbers)
Hard (Mostly Small Numbers)
Custom
Enter 4 Numbers (1-13)
Enter Your Solution
Supported Operators: + - × * / ÷ ( )
Check Answer
View Solution
Game Statistics
0
Solved
0
Total Puzzles
0%
Success Rate
Solution Result
Click to view answers and see all possible solutions
Game Rules
Use the given 4 numbers to reach 24 using addition, subtraction, multiplication, and division
Each number must be used exactly once
Parentheses can be used to change the order of operations
Supported operators: + - × * / ÷
Intermediate results can be fractions, but the final result must be 24
Classic Challenges
3 3 8 8 (Classic)
1 5 5 5 (Hard)
4 7 8 8 (Easy)
1 1 1 1 (No Solution)
2 7 10 10 (Medium)
Feature Description:
Auto Generate
:Automatically generate solvable 24-point puzzles based on difficulty
Answer Verification
:Enter your solution and the system will automatically check if it’s correct
View Solution
:If you can’t solve it, you can view all possible solutions
Custom Puzzle
:Enter any 4 numbers (1-13), and the system will determine if there's a solution
Multiple solutions available
:There may be multiple solutions for the same problem; the system will list them all
Game Statistics
:Track your solving history and success rate
Algorithm explanation:
Uses Depth-First Search (DFS) to explore all possible operation combinations
Permutes the 4 numbers and tries all combinations of 3 operators
Considers different bracket placements with 5 expression structures
Uses floating-point calculations; differences within 10⁻⁹ are considered equal
Automatically filters out duplicate equivalent solutions