S2T2

Jim Randell 4:42 pm on 5 January 2024 Permalink Reply
Tags: by: Stephen Hogg ( 62 )   

• 

  Jim Randell 5:05 pm on 5 January 2024 Permalink | Reply

  This Python program checks that the six Z numbers are all different (although this is not explicitly stated in the puzzle text, but it seems like a reasonable additional requirement).

  It runs in 55ms. (Internal runtime is 711µs).

  Run: [ @replit ]

  from enigma import (
    defaultdict, irange, tau, group, cproduct, primes,
    singleton, printf
  )
  
  # map Z numbers to code
  code = lambda z: (z % 8, tau(z))
  
  # group Z numbers by code
  g = group(irange(1, 91), by=code)
  
  # choose a sequence from the given codes
  codes = [(4, 6), (1, 4), (4, 6), (0, 6), (7, 2)]
  
  # collect possible sequences by (z3, z5) values
  d = defaultdict(list)
  for (z1, z2, z3, z4, z5) in cproduct(g[k] for k in codes):
    if len({z1, z2, z3, z4, z5}) != 5: continue
    # z5 is the lowest
    if not (z5 < min(z1, z2, z3, z4)): continue
    # z3 is the highest
    if not (z3 > max(z1, z2, z4, z5)): continue
    d[(z3, z5)].append((z1, z2, z3, z4, z5))
  
  # knowing z3 and z5 gives 15 possible sequences
  for (k, vs) in d.items():
    if len(vs) != 15: continue
    # consider possible prime z6 values
    for z6 in primes.between(1, 91):
      # look for matching sequences
      check = lambda z1, z2, z3, z4, z5: z2 < z6 < z1 and z6 != z4
      zs = singleton(zs for zs in vs if check(*zs))
      if zs is None: continue
      # output solution
      printf("z6={z6} -> zs={zs}")
  

  Solution: The catalyst has atomic number 47.

  The constituent elements (Z1..Z5) have atomic numbers: 52, 33, 68, 32, 7.

  So, the name of the drug is: TEASERGEN (= Te As Er Ge N).

  And the catalyst (Z6) has atomic number 47 (= Ag (Silver)).

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• 

  NigelR 12:48 pm on 7 January 2024 Permalink | Reply

  A bit convoluted but it seems to work!!

  from itertools import product
  
  def is_prime(n):
      if (n % 2 == 0 and n > 2) or n < 2: return False
      for i in range(3, int(n**0.5) + 1, 2):
          if n % i == 0: return False
      return True
  
  factno = lambda n: len([i for i in range(1, n + 1) if n % i == 0])
  zvals = lambda a,b: [i for i in range(1,92) if i%8 == a and factno(i) == b] 
  #Code values for z1 - z5
  Z = [[4,6], [1,4], [4,6], [0,6], [7,2]]
  #create dictionary d with lists of possible values for each element
  d = {i:zvals(x[0],x[1]) for i,x in enumerate(Z,1)}
  #create cand as list with valid sets of element values
  cand = []
  for x in (dict(zip(d.keys(), values)) for values in product(*d.values())):
      #z3 is highest, z5 is lowest and 5 different elements
      if x[3] != max(vals:= x.values()) or len(set(vals)) != 5 or x[5] != min(vals): continue
      else: cand.append(x)
  #remove duplicates and create list of valid x3 & x5
  z3z5 = [list(tupl) for tupl in {tuple(item) for item in [[x[3],x[5]] for x in cand]}]
  #Find z3z5 entry that has 15 possible sets
  res = [x for x in z3z5 if len([y for y in cand if y[3]==x[0] and y[5]==x[1]])==15 ]
  if len(res)>1 :
      print('unique solution not found')
      exit()
  else:
      res = res[0] #flatten res to list of selected x3 & x5
  #strip invalid sets from cand
  cand = [x for x in cand if x[3]==res[0] and x[5]==res[1]]
  z6lst=[]
  #look for possible prime values of z6 between z2 and z1
  for x in cand:
      if x[2]>x[1]:continue
      for y in range(x[2]+1,x[1]): 
          if is_prime(y):
              z6lst.append([y,x])
  z6set = [x[0] for x in z6lst]
  #look for singleton value of z6
  z6 = [x for x in z6set if z6set.count(x)==1]
  if len(z6)==1:
      z6 = z6[0]
  else:
      print('unique solution not found')
      exit()
  soltn = [x for x in z6lst if x[0]==z6][0]
  print(f'Catalyst atomic number was {soltn[0]}.')
  outstr = 'Z' + '  Z'.join([str(i)+' = '+ str(soltn[1][x]) for i,x in enumerate (soltn[1],1)])
  print('Element values were: ', outstr,'.')
  

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