S2T2

Jim Randell 9:55 am on 18 November 2025 Permalink Reply
Tags: by: Danny Roth ( 84 )   

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  Jim Randell 9:55 am on 18 November 2025 Permalink | Reply

  This Python program runs in 76ms. (Internal runtime is 238µs).

  from enigma import (defaultdict, subsets, tuples, printf)
  
  # solve for pairs <a> and <b>, next batsman <n>
  def solve(a=1, b=2, n=3, ts=list(), bs=list()):
    if n < 13:
      # total score when this pair ends
      t = a * b
      if ts and t < ts[-1]: return
      if n == 12:
        # either of the final pair is dismissed
        yield (ts + [t], bs + [(a, b)])
      else:
        # a is dismissed
        if not (a % 2 != 0 and bs and bs[-1] % 2 == 1):
          yield from solve(b, n, n + 1, ts + [t], bs + [a])
        # b is dismissed
        if not (b % 2 != 0 and bs and bs[-1] % 2 == 1):
          yield from solve(a, n, n + 1, ts + [t], bs + [b])
  
  # record scenarios by maximum pair score
  rs = defaultdict(list)
  
  # find possible scores
  for (ts, bs) in solve():
    # find the maximum score for a pair
    m = max(y - x for (x, y) in tuples(ts, 2))
    if not (m > 50): continue
    printf("[totals = {ts}; batsmen = {bs}; m = {m}]")
    rs[m].append((ts, bs))
  
  # choose max pair scores for visitors and home teams
  for (v, h) in subsets(sorted(rs.keys()), size=2):
    printf("\nmax pair: visitors = {v}, home = {h}")
    for (ts, bs) in rs[v]:
      printf("visitors: totals = {ts}; batsmen = {bs}")
    for (ts, bs) in rs[h]:
      printf("home: totals = {ts}; batsmen = {bs}")
  

  Solution: (a) The home team’s biggest stand was 81; (b) The result of the match was a tie (i.e. both teams achieved the same number of runs).

  The visitor’s scoresheet is one of the following:

  1 & 2: stand = 2; total = 2 [1 dismissed]
  2 & 3: stand = 4; total = 6 [2 dismissed]
  3 & 4: stand = 6; total = 12 [4 dismissed]

  or:

  1 & 2: stand = 2; total = 2 [2 dismissed]
  1 & 3: stand = 1; total = 3 [1 dismissed]
  3 & 4: stand = 9; total = 12 [4 dismissed]

  then:

  3 & 5: stand = 3; total = 15 [5 dismissed]
  3 & 6: stand = 3; total = 18 [6 dismissed]
  3 & 7: stand = 3; total = 21 [7 dismissed]
  3 & 8: stand = 3; total = 24 [8 dismissed]
  3 & 9: stand = 3; total = 27 [3 dismissed]
  9 & 10: stand = 63; total = 90 [10 dismissed]
  9 & 11: stand = 9; total = 99

  And the home team’s scoresheet is:

  1 & 2: stand = 2; total = 2 [2 dismissed]
  1 & 3: stand = 1; total = 3 [3 dismissed]
  1 & 4: stand = 1; total = 4 [4 dismissed]
  1 & 5: stand = 1; total = 5 [5 dismissed]
  1 & 6: stand = 1; total = 6 [6 dismissed]
  1 & 7: stand = 1; total = 7 [7 dismissed]
  1 & 8: stand = 1; total = 8 [8 dismissed]
  1 & 9: stand = 1; total = 9 [1 dismissed]
  9 & 10: stand = 81; total = 90 [10 dismissed]
  9 & 11: stand = 9; total = 99

  Each team has a final total of 99, and so the match is tied.

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