No puzzles this week; here are the results from the puzzles distributed
two weeks ago. (There's still plenty of time left on last week's
puzzle.)
On Tue, 2009-07-21 at 19:40 +0100, ais523 wrote:
> 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.)
> }}}
The only attempted answer to this was from root, who managed it in 8
weighings, the same as Murphy:
{{{
Weigh balls 1 and 2 against ball 3.
Weigh balls 2 and 4 against ball 6.
Weigh balls 2 and 5 against ball 7.
Weigh balls 2 and 8 against ball 10.
Weigh balls 2 and 9 against ball 11.
Weigh balls 2 and 12 against ball 14.
Weigh balls 2 and 13 against ball 15.
Weigh balls 2 and 16 against ball 18.
Ball 2 weighs 2 grams if and only if 4 or more of the measurements were
equal.
}}}
coppro claimed e would try to poke holes in any submitted answer;
however, this answer seems to allow for the fact that the four incorrect
balls might have any possible weight.
> "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?
> }}}
A lot more answers submitted to this one. Two different correct answers
were popularly submitted: 'flip switches 0, 3, 6' (Wooble, Murphy,
coppro), and 'flip all 9 switches' (root, Taral).
Time for the scoring, then. As neither puzzle had more than 6 correct
answers, the scoring for contestants is 4 x-points for the first correct
answer, 2 x-points for subsequent correct answers. Therefore, I award:
4 x-points to Wooble;
2 x-points to root;
4 x-points to root;
2 x-points to Murphy;
2 x-points to Taral;
2 x-points to coppro.
Contestmaster awards are 11 y-points, minus 1 for each eligible answer
(unless that would exceed points limit; in this case, it doesn't).
Therefore, I award:
10 y-points to Murphy;
5 y-points to Sgeo.
--
ais523
Enigma contestmaster
