@@ -2508,5 +2508,99 @@ def sol():
25082508 return [[p , q , r ] for p in primes for q in primes if p <= q for r in primes if q <= r and p * q * r < 1000 ]
25092509
25102510
2511+ class IntegerLog (PuzzleGenerator ):
2512+ """Inspired by [HumanEval](https://github.com/openai/human-eval) \\ #76"""
2513+ 2514+ @staticmethod
2515+ def sat (x : int , a = 3 , n = 1290070078170102666248196035845070394933441741644993085810116441344597492642263849 ):
2516+ """Find an integer exponent x such that a^x = n"""
2517+ return a ** x == n
2518+ 2519+ @staticmethod
2520+ def sol (a , n ):
2521+ m = 1
2522+ x = 0
2523+ while m != n :
2524+ x += 1
2525+ m *= a
2526+ return x
2527+ 2528+ def gen_random (self ):
2529+ a = self .random .randrange (1 , 10 )
2530+ n = a ** self .random .randrange (255 )
2531+ self .add (dict (a = a , n = n ))
2532+ 2533+ 2534+ class CubeRoot (PuzzleGenerator ):
2535+ """Inspired by [HumanEval](https://github.com/openai/human-eval) \\ #77
2536+
2537+ We made it harder by giving very large n for which `round(n ** (1/3))`
2538+ """
2539+ 2540+ @staticmethod
2541+ def sat (x : int , n = 42714774173606970182754018064350848294149432972747296768 ):
2542+ """Find an integer that when cubed is n"""
2543+ return x ** 3 == n
2544+ 2545+ @staticmethod
2546+ def sol (n ): # Using Newton's method
2547+ m = abs (n )
2548+ x = round (abs (n ) ** (1 / 3 ))
2549+ while x ** 3 != m :
2550+ x += (m - x ** 3 ) // (3 * x ** 2 )
2551+ return - x if n < 0 else x
2552+ 2553+ def gen_random (self ):
2554+ digits = self .random .randrange (30 )
2555+ n = self .random .randrange (- 10 ** digits , 10 ** digits ) ** 3
2556+ self .add (dict (n = n ))
2557+ 2558+ 2559+ 2560+ class HexPrimes (PuzzleGenerator ):
2561+ """Inspired by [HumanEval](https://github.com/openai/human-eval) \\ #78"""
2562+ 2563+ @staticmethod
2564+ def sat (primes : List [bool ], n = "A4D4455214122CE192CCBE3" ):
2565+ """Determine which characters of a hexidecimal correspond to prime numbers"""
2566+ return all (primes [i ] == (c in "2357BD" ) for i , c in enumerate (n ))
2567+ 2568+ @staticmethod
2569+ def sol (n ):
2570+ return [c in "2357BD" for c in n ]
2571+ 2572+ def gen_random (self ):
2573+ digits = self .random .randrange (30 )
2574+ n = hex (self .random .randrange (10 ** digits ))[2 :]
2575+ self .add (dict (n = n ))
2576+ 2577+ 2578+ class Binarize (PuzzleGenerator ):
2579+ """Inspired by [HumanEval](https://github.com/openai/human-eval) \\ #79"""
2580+ 2581+ @staticmethod
2582+ def sat (b : str , n = 5324680297138495285 ):
2583+ """Write n base 2 followed and preceded by 'bits'"""
2584+ assert b [:4 ] == b [- 4 :] == 'bits'
2585+ inside = b [4 :- 4 ]
2586+ assert all (c in "01" for c in inside )
2587+ assert inside [0 ] == "1" or len (inside ) == 1
2588+ m = 0
2589+ for c in inside :
2590+ m = 2 * m + int (c )
2591+ return m == n
2592+ 2593+ @staticmethod
2594+ def sol (n ):
2595+ s = bin (n )[2 :]
2596+ return f'bits{ s }
2597+ 2598+ def gen_random (self ):
2599+ digits = self .random .randrange (30 )
2600+ n = self .random .randrange (10 ** digits )
2601+ self .add (dict (n = n ))
2602+ 2603+ 2604+ 25112605if __name__ == "__main__" :
25122606 PuzzleGenerator .debug_problems ()
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