2009/4/16 Alex Smith <ais...@bham.ac.uk>: > On Tue, 2009-04-07 at 19:18 +0100, Alex Smith wrote: >> There was one Enigma puzzle this week, "Scales" by Tiger: >> > A puzzle named "Scales". >> > You have a balance scale and want to be able to measure any integer >> > number of ounces. Which is the biggest weight that you can measure >> > using four known masses, and still be able to measure each integer >> > number of ounces below it? Which four weights should you use? > > Well, this was certainly a popular puzzle! It's also had a very wide > range of answers, many of which were wrong, which is also unusual > (generally I only get correct answers or no answers). > > The answers I'm accepting as correct for this are 40 using 1, 3, 9, 27, > and 80 using 2, 6, 18, 54. The first is the "intended" answer that Tiger > submitted; the second is an improved answer based on an alternative > reading of the question (1, 3, 9, and 27 can for each integer 1-40 > determine whether an object has that weight; 2, 6, 18, and 54 can > determine the weight of an object with a weight from 1-80, given that > that weight is an integer). > > The first answer submitted was actually by the non-contestant Taral; > although it was correct, it does not count as an eligible answer because > Taral didn't join the contest by the end of the answer submission > period, so I award no points for it. > > I award 4 y-points to the submitter Tiger, as there was definitely at > least one eligible answer, though. (E'll also get two Clues.) > > The following answers were submitted by contestants: > 15 using 1, 2, 4, 8 by BobTHJ > I award 0 x-points to BobTHJ. > The problem with this, and all the other binary- > based answers, is that they don't exploit the > capability of putting weights on /both/ sides of > the balance scale. > 15 using 1, 2, 4, 8 by Billy Pilgrim > I award 0 x-points to Billy Pilgrim. > 30 using 2, 4, 8, 16 by root > I award 0 x-points to root. > root was the first to notice that you could > determine the weight of something known to have > integral weights by measuring only even weights; > however, this is incorrect due to not allowing > for weights on both sides of the scale. > 29 using 2, 3, 9, 17 by Wooble > I award 0 x-points to Wooble. > Nearly there! The problem is that 2 and 3 can't > make exactly 4 without help from an extra weight > so extra help is needed to make 13 with 2, 3, 9, > severely limiting the maximum available. > 15 using 1, 2, 4, 8 by Sgeo > I award 0 x-points to Sgeo. > 80 using 2, 6, 18, 54 by root > I award 8 x-points (and 2 Clues) to root. > Glad to see root correct eir earlier mistake! > 40 using 1, 3, 9, 27 /and/ > 80 using 2, 6, 18, 54 by Murphy > I award 4 x-points (and 1 Clue) to Murphy. > (Murphy was the only contestant to give the > answer under both possible interpretations.) > 33 using 1, 3, 8, 21 by coppro > I award 0 x-points to coppro. > Even more nearly there than Wooble... > 40 using 1, 3, 9, 27 by Sgeo > I award 4 x-points (and 1 Clue) to Sgeo. > Another contestant who corrected eir earlier > answer to handle weights on both sides. > (lots of answers) by comex > I award 0 x-points to comex. > An attempt to brute-force the puzzle by giving > a load of answers in the hope at least one is > correct. However, none of them was... > > In total, therefore, there were 3 eligible answers; and a whole load of > answers which were ineligible due to being incorrect. > > I award Tiger 2 y-points for each first-class active Enigma contestant > who did not submit a solution to eir puzzle (I believe this is Wooble, > me, comex, ehird, woggle, coppro, Dvorak, Rodlen = 8 players, or an > award of 16 y-points total, making a total of 20 when combined with the > 4 from earlier). > > Clues will be distributed shortly by private email, as always. You're > free to hoard them, share them, use them as bargaining chips, or > whatever. > > -- > ais523 > Contestmaster, Enigma > > Well, I didn't intend root's and Murphy's solutions, and I though they are clever in my opinion they take away what little connection to reality this puzzle has and made it only a puzzle. No wrong with that though, and I'm almost disappointed in myself for not thinking of it.
Also, the comment made early on about allowing negative weights making it not make any sense got me thinking - and since putting weights on both sides was half the solution there's nothing to prevent having, say, helium baloons whose buoyancy exactly matches the force exerted by one pound due to gravity. It does get a little ridiculous though. -- -Tiger
