S2T2

Jim Randell 10:32 am on 23 September 2025 Permalink Reply
Tags: by: Angela Newing ( 37 )   

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  Jim Randell 10:34 am on 23 September 2025 Permalink | Reply

  We can think of filling out a 5×5 binary matrix, indicating whether a person is one of the brothers, and which of the 4 tasks he can do.

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

  It runs in 133ms. (Internal runtime is 439µs).

  #! python3 -m enigma -rr
  
  SubstitutedExpression
  
  #     bro  vcm  dst  wsh  lnd
  #  J:  J    A    F    Q    V
  #  K:  K    B    G    R    W
  #  L:  L    C    H    S    X
  #  M:  M    D    I    T    Y
  #  N:  N    E    P    U    Z
  
  --base=2
  --distinct=""
  
  # there are 3 brothers (and 2 friends)
  "J + K + L + M + N == 3"
  
  # each brother can do exactly 2 tasks (and each friend exactly 3 tasks) [rows]
  --code="person = lambda b, *ts: sum(ts) == (2 if b else 3)"
  "person(J, A, F, Q, V)"
  "person(K, B, G, R, W)"
  "person(L, C, H, S, X)"
  "person(M, D, I, T, Y)"
  "person(N, E, P, U, Z)"
  
  # each task can be done by exactly 3 people [cols]
  --code="task = lambda *ps: sum(ps) == 3"
  "task(A, B, C, D, E)"
  "task(F, G, H, I, P)"
  "task(Q, R, S, T, U)"
  "task(V, W, X, Y, Z)"
  
  # exactly 1 brother knows how to vacuum
  "dot([J, K, L, M, N], [A, B, C, D, E]) == 1"
  
  # exactly 1 brother knows how to dust
  "dot([J, K, L, M, N], [F, G, H, I, P]) == 1"
  
  # L does not wash-up
  "S == 0"
  
  # exactly 1 person can wash-up and do the laundry
  "[Q + V, R + W, S + X, T + Y, U + Z].count(2) == 1"
  
  # there is 1 job both L and N can do
  "[C + E, H + P, S + U, X + Z].count(2) == 1"
  
  # there are 2 jobs K and N can do
  "[B + E, G + P, R + U, W + Z].count(2) == 2"
  
  # J can vacuum
  "A == 1"
  
  # M cannot vacuum
  "D == 0"
  
  # N is one of the brothers
  "N == 1"
  
  --template="(J A F Q V) (K B G R W) (L C H S X) (M D I T Y) (N E P U Z)"
  --solution=""
  --denest=-1
  --verbose="1-W"
  

  The following program can be used to give a more friendly output to the answer:

  from enigma import (SubstitutedExpression, seq2str, printf)
  
  # load the puzzle
  p = SubstitutedExpression.from_file(["{dir}/teaser2506.run"])
  
  # names
  names = ["John", "Keith", "Leo", "Mike", "Neil"]
  tasks = ["brother", "vacuum", "dust", "wash-up", "laundry"]
  results = ["JAFQV", "KBGRW", "LCHSX", "MDITY", "NEPUZ"]
  
  # solve the puzzle and format the solutions
  for s in p.solve(verbose=0):
    # output solution
    for (n, rs) in zip(names, results):
      # collect tasks
      ts = list(t for (t, v) in zip(tasks, rs) if s[v])
      printf("{n}: {ts}", ts=seq2str(ts, sep=", ", enc=""))
    printf()
  

  Solution: The other two brothers are: John and Mike. Keith, Leo and Neil can do dusting.

  The complete solution is:

  Brothers:
  John: vacuuming, laundry
  Mike: washing-up, laundry
  Neil: dusting, washing-up

  Friends:
  Keith: vacuuming, dusting, washing-up
  Leo: vacuuming, dusting, laundry

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    Frits 1:27 pm on 23 September 2025 Permalink | Reply

    The task function could also have been used instead of the person function.

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