S2T2

Jim Randell 7:29 am on 12 July 2022 Permalink Reply
Tags: by: Victor Bryant ( 140 )   

• 

  Jim Randell 7:30 am on 12 July 2022 Permalink | Reply

  (See also: Teaser 3009).

  In a round with n coins the points awarded are, the number of heads (+ bonus if guessed correctly) and the number of tails (+ bonus if guessed correctly). So n points are always awarded, along with 0, 1, or 2 bonuses.

  We don’t need to worry about the points won by each player, just the total number of points gained in each round.

  This Python program keeps a set of (total, bonus) pairs, and then progresses through the rounds keeping viable values.

  It runs in 57ms. (Internal runtime is 664µs).

  Run: [ @replit ]

  from enigma import (irange, is_prime, printf)
  
  # start with a total of 0, and all possible bonus values
  ss = set((0, x) for x in irange(0, 40))
  
  # start with <k> coins
  k = 7
  
  # consider subsequent rounds
  while k > 1:
    ss_ = set()
    # consider (total, bonus) in the previous round
    for (t, b) in ss:
      # consider number of bonuses awarded in this round
      for n in (0, 1, 2):
        t_ = t + k + n * b
        if is_prime(t_):
          ss_.add((t_, b))
    # move on to the next round
    (ss, k) = (ss_, k - 1)
  
  # output solutions
  for (t, b) in ss:
    printf("total = {t}, bonus={b}")
  

  Solution: The number of bonus points is 19. The total number of points at the end of the game is 103.

  The progression of the game is:

  7 coins: total = 7 (0 bonus points)
  6 coins: total = 13 (0 bonus points)
  5 coins: total = 37 (19 bonus points)
  4 coins: total = 79 (38 bonus points)
  3 coins: total = 101 (19 bonus points)
  2 coins: total = 103 (0 bonus points)

  LikeLike