PETRONODE - Letters and numbers

Letters and numbers

(Python 3.x)

Solve the TV number puzzles like a pro!

Popular in Australia SBS game.

This example demonstrates the power of Reverse Polish Notation (RPN) as well as the List Comprehension syntax.

The answer to the puzzle on the photo is (75 * 50 - 100 - 2) / 8 - 25 = 431

Or in RPN form: 75 ^ 50 * 100 - 2 - 8 / 25 - = 431

Download source code: Numbers_Solver.py

import time


class RPN_Calc:
    """
    Implements a simple RPN calculator
    Handles 5 operations: enter(^), plus, minus, multiply and divide
    """
    def __init__(self):
        self.Reset()
        return
    def Compute( self, Operand, Operator):
        self._Up()
        self.Stack[0] = Operand
        self.Equation += str( Operand)
        if Operator == '^':
            self.Equation += ' ^ '
            return self.Stack[0]
        if Operator == '+':
            self.Stack[0] += self.Stack[1]
            self._Down()
            self.Equation += ' + '
            return self.Stack[0]
        if Operator == '-':
            self.Stack[0] = self.Stack[1] - self.Stack[0]
            self._Down()
            self.Equation += ' - '
            return self.Stack[0]
        if Operator == '*':
            self.Stack[0] *= self.Stack[1]
            self._Down()
            self.Equation += ' * '
            return self.Stack[0]
        self.Equation += ' / '
        if self.Stack[0] <= 0 or (self.Stack[1] % self.Stack[0] != 0):
            self.Stack[0] = -999
            self._Down()
            return -999
        self.Stack[0] = int( self.Stack[1] // self.Stack[0])
        self._Down()
        return self.Stack[0]
    def Reset( self):
        self.Stack = [0,0,0,0,0,0]
        self.Equation = ""
        return
    def Result( self):
        return self.Stack[0]
    def PrintStack( self):
        for i in range(5,-1,-1):
            print( self.Stack[i])
        print()
        return
    def _Up(self):
        for i in range(5,0,-1):
            self.Stack[i] = self.Stack[i-1]
        return
    def _Down(self):
        for i in range(1,5):
            self.Stack[i] = self.Stack[i+1]
        self.Stack[5] = 0
        return


class Number_Solver:
    """
    Solves the classic "Letters and Numbers" game
    """
    def __init__(self, n=6):
        self.RPN = RPN_Calc()
        nums = ""
        for i in range(n): nums += str(i)
        self.Permutations = self.Create_Permutations( nums)
        self.Algorithms = []
        for p in self.Permutations:
            self.Algorithms += [p[0] + '^' + alg for alg in self.Create_Algorithms( p[1:])]
        return
    def Create_Permutations( self, nums):
        if len(nums)==1: return [nums[0]]
        tmp = []
        for c in nums:
            tmp += [c+num for num in self.Create_Permutations( nums.replace(c, ''))]
        return tmp
    def Create_Algorithms( self, permutation):
        if len(permutation) == 1: return [permutation[0] + o for o in "+-*/"]
        tmp = []
        c0 = permutation[0]
        algorithms = self.Create_Algorithms( permutation[1:])
        for o in "^+-*/":
            start = c0 + o
            tmp += [ start + alg for alg in algorithms]
        return tmp
    def RunAlgorithm( self, operands, algorithm, target):
        self.RPN.Reset()
        for i in range(0, len(algorithm), 2):
            operand = algorithm[i]
            operator = algorithm[i+1]
            r = self.RPN.Compute( operands[int(operand)], operator)
            if r < 0: break
            if r == target: break
        return self.RPN.Result()
    def SolveTarget( self, operands, target):
        self.Target = target
        self.Result = 0
        self.Mindiff = target
        self.Solution = "No solution found"
        for a in self.Algorithms:
            r = self.RunAlgorithm(operands, a, target)
            if r < 0: continue
            diff = target - r
            if diff < 0: diff = -diff
            if diff == 0:
                self.Mindiff = 0
                self.Result = target
                self.Solution = self.RPN.Equation.strip()
                return
            if diff > self.Mindiff: continue
            self.Mindiff = diff
            self.Result = r
            self.Solution = self.RPN.Equation.strip()
        return    
    def ReportSolution( self):
        if self.Mindiff == 0:
            print( "Exact solution found:")
            print( self.Solution + ' = ' + str(self.Result))
            return
        if self.Mindiff < 10:
            print( "Solution within the scoring range:")
        else:
            print( "Cannot do any better:")
        print( self.Solution + ' = ' + str(self.Result) + ' (' + str(self.Mindiff) + ' off)')
        return

                
ns = Number_Solver()
#for i, p in enumerate(ns.Permutations):
#    print(i+1, p)
#for i, a in enumerate(ns.Algorithms):
#    print(i+1, a)

print("Solving Letters and Numbers by RPN calc!")
print()

while True:
    nums = input( "Input numbers (with space): ")
    if len(nums) == 0: break
    #nums = "10 25 1 2 9 3"
    targ = input( "Input Target: ")
    if len(targ) == 0: break
    #targ = "253"
    try:
        operands = [int(n) for n in nums.split(' ')]
        if len(operands) < 6:
            print("Not enough numbers")
            continue
        target = int(targ)
    except:
        print("Must be an Integer")
        continue
    t = time.process_time()
    ns.SolveTarget(operands, target)
    ns.ReportSolution()
    print( "Solved in {:.3f} seconds".format(time.process_time() - t))
    print()


Home Software Manuals Training Codelets Iterative Density Porosity Archie S_wa Triangle Solver Height by Triangulation Object Size by Triangulation Nelder-Mead Optimization Letters and numbers Mission Papers Links Contacts	Letters and numbers (Python 3.x) Solve the TV number puzzles like a pro! Popular in Australia SBS game. This example demonstrates the power of Reverse Polish Notation (RPN) as well as the List Comprehension syntax. The answer to the puzzle on the photo is *(75 50 - 100 - 2) / 8 - 25 = 431 Or in RPN form: 75 ^ 50 * 100 - 2 - 8 / 25 - = 431 Download source code: Numbers_Solver.py** import time class RPN_Calc: """ Implements a simple RPN calculator Handles 5 operations: enter(^), plus, minus, multiply and divide """ def __init__(self): self.Reset() return def Compute( self, Operand, Operator): self._Up() self.Stack[0] = Operand self.Equation += str( Operand) if Operator == '^': self.Equation += ' ^ ' return self.Stack[0] if Operator == '+': self.Stack[0] += self.Stack[1] self._Down() self.Equation += ' + ' return self.Stack[0] if Operator == '-': self.Stack[0] = self.Stack[1] - self.Stack[0] self._Down() self.Equation += ' - ' return self.Stack[0] if Operator == '': self.Stack[0] = self.Stack[1] self._Down() self.Equation += ' * ' return self.Stack[0] self.Equation += ' / ' if self.Stack[0] <= 0 or (self.Stack[1] % self.Stack[0] != 0): self.Stack[0] = -999 self._Down() return -999 self.Stack[0] = int( self.Stack[1] // self.Stack[0]) self._Down() return self.Stack[0] def Reset( self): self.Stack = [0,0,0,0,0,0] self.Equation = "" return def Result( self): return self.Stack[0] def PrintStack( self): for i in range(5,-1,-1): print( self.Stack[i]) print() return def _Up(self): for i in range(5,0,-1): self.Stack[i] = self.Stack[i-1] return def _Down(self): for i in range(1,5): self.Stack[i] = self.Stack[i+1] self.Stack[5] = 0 return class Number_Solver: """ Solves the classic "Letters and Numbers" game """ def __init__(self, n=6): self.RPN = RPN_Calc() nums = "" for i in range(n): nums += str(i) self.Permutations = self.Create_Permutations( nums) self.Algorithms = [] for p in self.Permutations: self.Algorithms += [p[0] + '^' + alg for alg in self.Create_Algorithms( p[1:])] return def Create_Permutations( self, nums): if len(nums)==1: return [nums[0]] tmp = [] for c in nums: tmp += [c+num for num in self.Create_Permutations( nums.replace(c, ''))] return tmp def Create_Algorithms( self, permutation): if len(permutation) == 1: return [permutation[0] + o for o in "+-/"] tmp = [] c0 = permutation[0] algorithms = self.Create_Algorithms( permutation[1:]) for o in "^+-/": start = c0 + o tmp += [ start + alg for alg in algorithms] return tmp def RunAlgorithm( self, operands, algorithm, target): self.RPN.Reset() for i in range(0, len(algorithm), 2): operand = algorithm[i] operator = algorithm[i+1] r = self.RPN.Compute( operands[int(operand)], operator) if r < 0: break if r == target: break return self.RPN.Result() def SolveTarget( self, operands, target): self.Target = target self.Result = 0 self.Mindiff = target self.Solution = "No solution found" for a in self.Algorithms: r = self.RunAlgorithm(operands, a, target) if r < 0: continue diff = target - r if diff < 0: diff = -diff if diff == 0: self.Mindiff = 0 self.Result = target self.Solution = self.RPN.Equation.strip() return if diff > self.Mindiff: continue self.Mindiff = diff self.Result = r self.Solution = self.RPN.Equation.strip() return def ReportSolution( self): if self.Mindiff == 0: print( "Exact solution found:") print( self.Solution + ' = ' + str(self.Result)) return if self.Mindiff < 10: print( "Solution within the scoring range:") else: print( "Cannot do any better:") print( self.Solution + ' = ' + str(self.Result) + ' (' + str(self.Mindiff) + ' off)') return ns = Number_Solver() #for i, p in enumerate(ns.Permutations): # print(i+1, p) #for i, a in enumerate(ns.Algorithms): # print(i+1, a) print("Solving Letters and Numbers by RPN calc!") print() while True: nums = input( "Input numbers (with space): ") if len(nums) == 0: break #nums = "10 25 1 2 9 3" targ = input( "Input Target: ") if len(targ) == 0: break #targ = "253" try: operands = [int(n) for n in nums.split(' ')] if len(operands) < 6: print("Not enough numbers") continue target = int(targ) except: print("Must be an Integer") continue t = time.process_time() ns.SolveTarget(operands, target) ns.ReportSolution() print( "Solved in {:.3f} seconds".format(time.process_time() - t)) print()
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