Brain-Teaser 518: [Prophecies]
From The Sunday Times, 16th May 1971 [link]
An interesting fragment tells us what took place at the meeting of the Five Prophets:
“If Hosea hath prophesied truth, Micah and Obadiah will die in the same city; if Micah hath prophesied truth, Joel and Obadiah will die in the same city. It is the saying of Joel that three of the five prophets shall die in Babylon; and Nahum declareth to Hosea that the two of them shall die in different cities.”
It is well known that those who prophesy correctly die in Jerusalem, whereas those who make false prophecies die in Babylon.
So how many of these five will die in Jerusalem?
This puzzle was originally published with no title.
[teaser518]
John Crabtree and 
S2T2 
Jim Randell 8:22 am on 21 April 2020 Permalink |
There are only 2^5 (= 32) possibilities, so we can examine them all.
This Python program runs in 79ms.
from enigma import subsets, printf # check statement made by X check = lambda X, s: (X == "J") == bool(s) # consider where each will die for (H, J, M, N, O) in subsets("BJ", size=5, select="M"): # how many die in J? n = (H, J, M, N, O).count('J') # "H: M and O will die in the same city" if not check(H, M == O): continue # "M: J and O will die in the same city" if not check(M, J == O): continue # "J: [exactly] three of the five prophets shall die in B" if not check(J, n == 2): continue # "N: N and H shall die in different cities" if not check(N, N != H): continue # output solution printf("n={n} [H={H} J={J} M={M} N={N} O={O}]")Solution: One of them will die in Jerusalem.
There are two solutions:
We are not given a prophesy by O, to verify whether it is true or not, but we can infer where he must die in order for the prophecies we are given to be consistent, and from that whether he makes prophecies that are true or false.
In the first case he must die in Jerusalem, so must make true prophecies. And in the second case he must die in Babylon, and so must make false prophecies.
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John Crabtree 8:18 pm on 22 April 2020 Permalink |
Let the prophesies be #1, #2, #3 and #4 by H, M, J and N respectively.
From #4, H dies in Babylon.
Then from #1, one, and only one, of M and O die in Babylon.
Then from #2, J dies in Babylon.
Then from #3, four prophets, including N, die in Babylon.
And so one prophet (Micah or Obadiah) dies in Jerusalem.
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