TARGET = 34 
 KADD1, KADD2, KMUL = 1, 2, 2 
  
 def gameOver( n1 ): 
   return n1 >= TARGET 
  
 def nextVariants( x, previousMove ): 
    nextCodes = [(gameResult( x+KADD1, 1 ), 1), 
                 (gameResult( x+KADD2, 2 ), 2), 
                 (gameResult( x*KMUL, 3 ), 3) ] 
    return [ code for code in nextCodes 
                  if code[1] != previousMove ] 
  
 results = {}              
 def gameResult( x, previousMove = -1 ): 
   print( x, previousMove ) 
   if (x, previousMove) in results: 
     return results[(x, previousMove)]      
   if gameOver(x): return 0 
   nextCodes = nextVariants( x, previousMove ) 
   negative = [c for c in nextCodes if c[0] <= 0] 
   if negative: 
     move = max( negative, key = lambda x: x[0] ) 
     res = - move[0] + 1 
   else: 
     move = max( nextCodes, key = lambda x: x[0] ) 
     res = - move[0] 
   results[(x, previousMove)] = res	 
   return res 
  
 from math import ceil 
 ans1 = ceil( TARGET/KMUL - 1 ) 
 ans2 = [] 
 ans3 = [] 
 for S in range(TARGET-1,0,-1): 
   r = gameResult( S ) 
   print( "%d: %d" % (S, r) ) 
   if r == 2: ans2.append(S) 
   if r == -2: ans3.append(S) 
  
 #------------------------------------------------------- 
 # Ответы на вопросы 
 #------------------------------------------------------- 
 print("--- Ответы на вопросы ---") 
 print("1. ", ans1) 
 print("2. ", sorted(ans2)) 
 print("3. ", sorted(ans3))

def f(x,p): 
     if x>=100 and p==4: 
         return True 
     else: 
         if x<100 and p==4: 
             return False 
         else: 
             if x>=100: 
                 return False 
     if p%2==0: 
         return f(x+1,p+1) 
     else: 
         return f(x+3,p+1) or f(x*3,p+1) 
     if p%2==0: 
         return f(x+3,p+1) 
     else: 
         return f(x*3,p+1)or f(x+1,p+1) 
     if p%2==0: 
         return f(x*3,p+1) 
     else: 
         return f(x+3,p+1) or f(x+1,p+1) 
             
 for s in range(1,99): 
     if f(s,1): 
         print(s) 
 print('====================================') 
 def f(x,p): 
     if x>=100 and p==2: 
         return True 
     else: 
         if x<100 and p==2: 
             return False 
         else: 
             if x>=100: 
                 return False 
     if p%2==0: 
         return f(x+1,p+1) 
     else: 
         return f(x+3,p+1) or f(x*3,p+1) 
     if p%2==0: 
         return f(x+3,p+1) 
     else: 
         return f(x*3,p+1)or f(x+1,p+1) 
     if p%2==0: 
         return f(x*3,p+1) 
     else: 
         return f(x+3,p+1) or f(x+1,p+1) 
             
 for s in range(1,99): 
     if f(s,1): 
         print(s)