Re: [s-b] [s-d] Poor Durdenians

["Jamie Dallaire" <bad.leprechaun@xxxxxxxxx>]

Below is Wooble's elegant, and correct, answer to the riddle. Wooble
officially wins.

I give Wooble m80.
I give Murphy m10. (he answered it last night)

Billy Pilgrim

ps: Muddy children problem? Probably. I originally encountered it as a
problem about observant wives kicking out their cheating husbands but had to
dress it up to avoid people just googling the answer.
---------------------------
10 WRAs leave their buildings 9.5 Gloobhours after the beacon lit up.

For any time n Gloobhours after a beacon lights, n+1 Durdenians can
deduce correctly that their airlocks are damaged.

Proof by the axiom of induction:
n = 0: If exactly one airlock is damaged, the resident of the damaged
building knows:
1) At least one airlock is damaged because the beacon has lit, and
2) No other airlock is damaged because he can see them all.
3) Therefore, his own airlock is the damaged one.

n = 1: If two airlocks are damaged, the resident of a damaged buildings
knows:
1) One other airlock is damaged because he can see it.
2) The one he can see isn't the only one damaged; if it was the
Durdenian living there would have deduced it immediately and repaired
it half a Gloobhour ago.
3) Therefore, his own airlock is damaged.

For each additional damaged airlock, the above logic applies; each
resident of a damaged building knows that if his own airlock were
undamaged, the others would have all deduced the damage one Gloobhour
earlier.

Therefore, 9 hours after the beacon lit, 10 Durdenians deduced that
their airlocks were damaged and half an hour later sent out their WRAs
to repair the damage.

--Wooble
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