S2T2

Jim Randell 6:46 am on 31 August 2025 Permalink Reply
Tags: by: Andrew Skidmore ( 85 )   

• 

  Jim Randell 7:04 am on 31 August 2025 Permalink | Reply

  Here is a solution using the [[ SubstitutedExpression ]] solver from the enigma.py library.

  This run file executes in 154ms. (Internal runtime of the generated code is 4.7ms).

  #! python3 -m enigma -rr
  
  SubstitutedExpression
  
  # opponents scores in each innings are 3-digit square numbers
  "is_square(ABC)"  # = first innings
  "is_square(DEF)"  # = second innings
  # and their total number of runs is also a square number
  "is_square(ABC + DEF)"  # = opponents total
  
  # setters first and second innings score are 3-digit prime numbers
  "is_prime(UVW)"  # = first innings
  "is_prime(XYZ)"  # = second innings
  
  # setters team took the lead after their first innings
  "UVW > ABC"
  
  # after the opponents second innings the setters team trailed
  # by a 3-digit prime number of runs (= RST; < 250)
  "ABC + DEF - UVW = RST"
  "is_prime(RST)"
  "RST < 250"
  
  # but the setters team lost the match by a prime number of runs
  "is_prime(ABC + DEF - UVW - XYZ)"
  
  # distinct digits
  --distinct="ABCDEF,RSTUVW"
  
  # required answer is XYZ
  --answer="XYZ"
  
  # [optional] neaten up output
  --template="ABC UVW DEF XYZ" # scores in each innings
  --solution=""
  

  Solution: In the second innings, the setters team scored 239 runs.

  The opponents scores were 324 and 576 (both square numbers, and the sum is 900, also a square number), but we don’t know which order they were scored in.

  The setters team scores 659 (a prime number) in their first innings (and so were in lead lead after their first innings, but behind by 241 (a prime number) after the opponents second innings.

  In their second innings, the setters team scored 239 (a prime number), which gives them a total of 898, so they lost the game by 2 runs (a prime number).

  LikeLike

  • 

    Ruud 2:51 pm on 31 August 2025 Permalink | Reply

    import peek
    import istr
    
    for they1, they2 in istr.product((x for x in istr.range(100, 1000) if x.is_square()), repeat=2):
        if (they1 + they2).is_square() and (they1 | they2).all_distinct():
            for us1, us2 in istr.product((x for x in istr.range(100, 1000) if x.is_prime()), repeat=2):
                if us1 > they1:
                    score3 = they1 + they2 - us1
                    if score3.is_prime() and len(score3) == 3 and score3 < 250:
                        if (they1 + they2 - us1 - us2).is_prime():
                            if (score3 | us1).all_distinct():
                                peek(they1, they2, us1, us2)
    

    LikeLike

• 

  GeoffR 8:48 am on 2 September 2025 Permalink | Reply

  As an exercise, this posting is formatted to PEP-8 or the Python Enhancement Proposal. It does seem to make code more organised and readable. I used Jim’s names for variables.

  from enigma import is_prime
  
  # three digit primes 
  primes = [n for n in range(101, 1000, 2) if is_prime(n)]
  # three digit squares
  sq3 = [x ** 2 for x in range(10, 32)]
  # squares up to 2000
  sq34 = [x ** 2 for x in range(10, 44)]
  
  # opponents first score
  for ABC in sq3:
    A, B, C = (int(x) for x in str(ABC))
    if len(set(str((ABC)))) == 3:
      
      # our first score
      for UVW in primes:
        if UVW <= ABC:
          continue
        U, V, W = (int(x) for x in str(UVW))
        
        # opponents second score
        for DEF in sq3:
          if DEF == ABC or ABC + DEF not in sq34:
            continue
          
          # ABC and DEF combined have six different digits
          D, E, F = (int(x) for x in str(DEF))
          if len(set((A, B, C, D, E, F))) != 6:
            continue
          
          # after second score
          if not (100 < (RST := ABC + DEF - UVW) < 250 and is_prime(RST)):
            continue
         
          # UVW and RST combined have six different digits
          R, S, T = (int(x) for x in str(RST))
          if len(set((U, V, W, R, S, T ))) != 6:
            continue
  
          # our second score
          for XYZ in primes:
            # we lost the match by a prime number of runs
            if XYZ != UVW and is_prime(ABC + DEF - UVW - XYZ):
              print(f"Home team scores(1st and 2nd): {UVW} and {XYZ}.")
              print(f"Visiting team scores(1st and 2nd): {ABC} and {DEF}.")
              print()
  
  

  LikeLike