Brain-Teaser 487: [Seating arrangements]
From The Sunday Times, 27th September 1970 [link]
Five friends, Archer, Brown, Carter, Dale and Eade, and their wives, Anne, Betty, Clara, Diana and Edna, meet on the first Wednesday of every month to dine together (at a round table) in a local hotel. They have a rule that no wife may sit next to, or immediately opposite, her husband. Archer, as M.C., sits always with his back to the fireplace.
We are concerned with the seating arrangements in January, April, July and October. On these four occasions no man, with the exception of the M.C., sat at any place more than once. In January the men sat in clockwise alphabetical order (men and women always sit alternately). Also, on these four evenings, the ladies sitting opposite Archer were successively: Betty, Clara, Diana and Edna.
In April, Diana sat at the same place she occupied in January, and in July, Anne sat at the same place that she occupied in April.
What was the seating arrangement in October? (Clockwise, A to A, using capital initials for the men and small initials for the women).
This puzzle was originally published with no title.
[teaser487]
GeoffR and 
Lise Andreasen and 
John Crabtree and 
S2T2 
Jim Randell 3:14 pm on 18 July 2019 Permalink |
This Python program runs in 88ms.
Run: [ @repl.it ]
from enigma import subsets, update as _update, join, printf # possible names names = "ABCDE" # update a string with new items def update(s, js, vs): return join(_update(list(s), js, vs)) # generate possible seating plans def generate(ss): # find unseated people, and empty places (xs, js) = (set(names), list()) for (j, x) in enumerate(ss): if x == '?': js.append(j) else: xs.remove(x) # complete the seating plan for s in subsets(xs, size=len, select='P'): yield update(ss, js, s) # groups of adjacent and opposite seats: w -> m group = { 0: [0, 1, 3], 1: [1, 2, 4], 2: [2, 3, 0], 3: [3, 4, 1], 4: [4, 0, 2], } # check no men reuse seats, apart from seat 0 def m_check(ms, ss): for (i, x) in enumerate(ms): if i == 0: continue if any(s[i] == x for (s, _) in ss): return False return True # check no woman is seated opposite or next to her husband def w_check(ms, ws): for (i, w) in enumerate(ws): if any(ms[j] == w for j in group[i]): return False return True # find seating plans, given previous plans def solve(ms, ws, ss=[]): # complete the seating plan for the men for ms1 in generate(ms): if not m_check(ms1, ss): continue # complete the seating plan for the women for ws1 in generate(ws): if not w_check(ms1, ws1): continue yield (ms1, ws1) # find the January seating plan for Jan in solve('ABCDE', '??B??'): # find the April seating plan # Mrs D sits in the same place as in Jan ws = update('??C??', [Jan[1].index('D')], ['D']) for Apr in solve('A????', ws, [Jan]): # find the July seating plan # Mrs A sits in the same place as in April ws = update('??D??', [Apr[1].index('A')], ['A']) for Jul in solve('A????', ws, [Jan, Apr]): # find the October seating plan for Oct in solve('A????', '??E??', [Jan, Apr, Jul]): # output the seating plans printf("Jan={Jan[0]}+{Jan[1]} Apr={Apr[0]}+{Apr[1]} Jul={Jul[0]}+{Jul[1]} Oct={Oct[0]}+{Oct[1]}")Solution: The seating arrangement in October was:
The other seating plans are:
In places where there are options either the first or second option is used consistently throughout.
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