0 20 puzzle

The 0-20 puzzle is a mathematical challenge where you use the digits 0 through 9 exactly once (or sometimes repeated, depending on the rules) to construct equations that equal every number from 0 to 20. Here's how it works: Basic Rules: Use each digit 09 exactly once (unless repetition is allowed). Combine digits to form multi-digit numbers (e.g., "12" from 1 and 2). Allowed operations: +, , , , exponents, factorials, decimals, concatenation (e.g., "1" + "2" = "12"), and sometimes square roots or other functions. Parentheses can be used to dictate order of operations. Example Solutions for 020: Here are some creative ways to solve the puzzle (solutions may vary): 0: ( 0 imes (1 + 2 + 3 + dots + 9) ) 1: ( (9 - 8) imes (7 - 6) imes dots imes (1 - 0) ) 2: ( 1 + 2 + 3 - 4 - 5 + 6 - 7 + 8 - 9 + 0 ) 3: ( (9 + 0) (1 + 2) ) 4: ( 1 + 3 + 5 + 7 - 2 - 4 - 6 - 8 + 9 + 0 ) 5: ( (1 + 2 + 3 + 4) - (5 + 6 + 7 - 8 - 9 - 0) ) 6: ( 9 - 8 + 7 - 6 + 5 - 4 + 3 - 2 + 1 - 0 ) 7: ( (9 imes 1) - (8 imes 0) - 2 ) 8: ( 9 - 1 + 0 ) (using only 3 digits; adjust as needed) 9: ( 9 imes (1 + 0) ) 10: ( 9 + 1 + 0 ) 11: ( 9 + 2 + 0 ) 12: ( 9 + 3 + 0 ) or ( (9 imes 1) + 2 + 0 ) 13: ( 9 + 4 + 0 ) 14: ( 9 + 5 + 0 ) 15: ( 9 + 6 + 0 ) 16: ( 9 + 7 + 0 ) 17: ( 9 + 8 + 0 ) 18: ( 9 + 8 + 1 + 0 ) 19: ( 10 + 9 + 0 ) (using "10" as a concatenated number) 20: ( 10 + 9 + 1 + 0 ) or ( (5 imes 4) + 0 ) Advanced Variations: Factorials/Exponents: Use ( 3! = 6 ) or ( 23 = 8 ) for more compact solutions. Example for 20: ( (5 imes 4) + (0 imes ext{other digits}) ). Decimals: ( 1.2 + 3.4 + dots ). Square Roots: ( sqrt{9} = 3 ). Would you like solutions for a specific number or a stricter set of rules? Let me know!