#
# PYTHON • MyCompiler
# Quebra Cuca | Puzzle
# https://[Log in to view URL]
# Cálculo das Soluções
# 
# 2026 Maio Qua, 13 — Sáb, 16
# by 
# j
# 

import random
import matplotlib.pyplot as plt
import numpy as np

#
# W A R N I N G 
#
# Para obter todas as 8105 soluções 
# deste puzzle é necessário configurar 
# a variável MAX para 5000000; no 
# entanto haverá a necessidade de mudar 
# a ambiência de execução deste código 
# python para evitar o estouro de tempo.
#
# To obtain all 8,105 solutions to this 
# puzzle, you must set the MAX variable 
# to 5,000,000; however, you will need 
# to adjust the execution environment 
# for this Python code to avoid a 
# timeout.
#

MAX = 20

line = []

def carga():

  print("")
  print("... Carga Das Triplas ...")
  print("")
    
  max = 9

  h = 0
  for x in range(1,max+1):
     for y in range(1,max+1):
        for z in range(1,max+1):
        
           s = x + y + z
    
           if (s == 19):
              
              t = str(x) + ':' + str(y) + ':' + str(z)
              r = '(' + str(x) + ',' + str(y) + ',' + str(z) + ')'
      
              if not(t in line):
              
                 line.append(t)

                 h += 1
                  
                 if (h < 45):
                     print(r,end=',')
                 else:
                     print(r)
    
  print("")
  print(len(line)," Triplas Carregadas")
  print("")

def search(num,pos):
    
    f = True
    
    while (f):
        
        v = random.randint(1,45)
  
        x = int(line[v-1][0])
        y = int(line[v-1][2])
        z = int(line[v-1][4])

        u = ( pos == 1 ) and (x == num)
        v = ( pos == 2 ) and (y == num)
        h = ( pos == 3 ) and (z == numpy)

        if ( u or v or h ):
        
           f = False
        
    t = str(x) + ':' + str(y) + ':' + str(z)
    
    return t

def graf(s):

    plt.style.use('dark_background')

    leg = "e:d:b:c:i:f:g:a:j:h"

    num = []
    for i in range(0,10):
        num.append(s[0][2*i])
        
    cx = []
    cy = []

    R = 10
    konst = (2*np.pi)/5
    delta = 55*np.pi/180

    for j in range(0,5):

        cx.append(R*np.cos(j*konst+delta))
        cy.append(R*np.sin(j*konst+delta))

    R = 24
    
    konst = (2*np.pi)/5
    delta = 20*np.pi/180

    for j in range(0,5):

        cx.append(0+R*np.cos(j*konst+delta))
        cy.append(0+R*np.sin(j*konst+delta))

    x = []
    y = []

    raio = 1.5
    
    plt.figure(figsize=(6,6))

    teta = np.linspace(0, 2*np.pi, 100)

    for j in range (0,10):
        
        x.append(cx[j] + raio * np.cos(teta))
        y.append(cy[j] + raio * np.sin(teta))

        plt.plot(x[j], y[j])

    for j in range(0,4):
        
        plt.plot([cx[j],cx[j+1]],[cy[j],cy[j+1]])

    plt.plot([cx[4],cx[0]],[cy[4],cy[0]])
    plt.plot([cx[4],cx[8]],[cy[4],cy[8]])
    plt.plot([cx[4],cx[8]],[cy[4],cy[8]])

    plt.plot([cx[0],cx[9]],[cy[0],cy[9]])
    plt.plot([cx[1],cx[5]],[cy[1],cy[5]])
    plt.plot([cx[2],cx[6]],[cy[2],cy[6]])
    plt.plot([cx[3],cx[7]],[cy[3],cy[7]])

    for j in range(0,10):
        plt.scatter(cx[j],cy[j], s=400, alpha=1, color="black")
        plt.text(cx[j]-0.5,cy[j]-0.5,num[j],color="w")
        plt.text(cx[j]-0.50,cy[j]-3.25,leg[2*j],color="w")
    
    tit = 'Puzzle | ' + s[0]

    plt.axis('equal') 
    plt.title(tit)
    plt.xticks([])  
    plt.yticks([])
    plt.grid(False)
    plt.show()

def ultra():

  carga()

  print("... Solução Ultra ...")
  print("")
  
  sol = []

  z = 1
  
  while (z < MAX):

    v = random.randint(1,45)
  
    a = int(line[v-1][0])
    b = int(line[v-1][2])
    c = int(line[v-1][4])

    r = search(b,1)
  
    b = int(r[0])
    d = int(r[2])
    g = int(r[4])
    
    r = search(d,1)
  
    d = int(r[0])
    e = int(r[2])
    f = int(r[4])

    r = search(e,1)
  
    e = int(r[0])
    i = int(r[2])
    h = int(r[4])
  
    j = 19 - (c + i)
    
    k = ( (a+b+c) == 19 )
    l = ( (b+d+g) == 19 )
    m = ( (d+e+f) == 19 )
    n = ( (e+i+h) == 19 )
    o = ( (i+c+j) == 19 )
    p = ( j <= 9 )
    
    if ( k and l and m and n and o and p ):
    
       t = str(e) + ':' + str(d) + ':' + str(b) + ':' + str(c) + ':' + str(i) + ':' + str(f) + ':' + str(g) + ':' + str(a) + ':' + str(j) + ':' + str(h)
        
       if not(t in sol):
       
         sol.append(t)
        
    z += 1
  
  print(sol)
  print("")
  print("quantidade = ",len(sol))

  return sol

def contagem():
    
    carga()
    
    max = 1000
    
    tipo = []
    cont = [0,0,0,0,0,0,0,0,0]
    
    sum = 0
    
    for j in range(1,10):
        
        print("... Análise "+str(j)+" ...")
        
        tipo.clear()
        k = 0
        s = 0
        while (k < max):
            t = search(j,2)
            if (int(t[2]) == j):
                if (not(t in tipo)):
                    tipo.append(t)
                    print(t)
                    s += 1
            k += 1
        m = s
        print("Total = ",m)
        print("")

        tipo.clear()
        k = 0
        s = 0
        while (k < max):
            t = search(j,1)
            if (int(t[0]) == j):
                if (not(t in tipo)):
                    tipo.append(t)
                    print(".....",t)
                    s += 1

                    #
                    # Conta meio
                    #

                    cont[int(t[2])-1] += 1

            k += 1
        n = s
        print("Total = ",n)
        print("")

        sum += m*n

    print("Total Geral = ",sum)
    print(cont)

def control():
    s = ultra()
    graf(s)
    
#contagem()
control()