I accidentally forgot to send out the puzzles last week; so this week
will have last week's puzzles as well as its own. (I'll be punished for
this by not getting contestmaster pay this month; if anyone else wants
to take over Enigma for me for this horrible mistake, feel free to
submit an intent.)
There are two puzzles this week; "Twenty Balls" by Murphy and "Nine
Switches" by Sgeo.
"Twenty Balls" by Murphy:
{{{
You have twenty balls, labeled 1 to 20. Exactly 16 of them weigh a
number of grams equal to their number. Using only a simple balance
scale, and as few weighings as possible, determine whether the ball
labeled 2 weighs 2 grams. (Disclaimer: I think my solution is optimal
but I'm not sure, so any solution that uses at most that many weighings
should get credit.)
}}}
"Nine Switches" by Sgeo:
{{{
Nine switches (not Agoran switches), 0-8, are arranged in a circle
such that a switch n is across from switches (n+4 (mod 9)) and (n+5
(mod 9))
When a switch is switched manually, the switches across from it are
also switched. The switches that were not switched manually by this do
not cause the switches across from them to switch.
The switches all start out off. What switches need to be manually
switched, how many times, and in what order, in order for all switches
to be on?
}}}
Anyone can submit answers; you have one week from now. Even if you
aren't an Enigma contestant now, you can score if you join Enigma by the
time the answer submission period ends a week from now, and are a player
of Agora at the time I award points. Only the /last/ answer you submit
counts (so you can change your mind, but not brute-force the puzzles).
As there are 2 puzzles announced this week, the first correct answer on
each puzzle will score 4 x-points, and subsequent correct answers will
score 2 x-points; if /more than 6/ answers are submitted on either or
both puzzles, all awards to players for that puzzle will be reduced by 1
x-point.
For each puzzle, the author will get 11 y-points, minus 1 for every
contestant who submits a correct answer. An exception is that 0 points
will be awarded if nobody gets it right.
Happy puzzling, everyone!
--
ais523
Enigma contestmaster
