Welcome back for our [tear, cry] last issue of the term. If you're wondering, no, Five does not actually rhyme with Monkeys, but I used the Johnny Five joke in the Fall, and Jive in the Summer, so in the immortal words of not-Sean Connery, "Suck it, Trebek."
Interestingly enough, no one got both of the coin problems right. In fact, only one person got A, and a different person got B. The common errors were splitting piles in half instead of thirds for B, and trying a similar method of splitting the problem for A. As is her policy, everyone who attempted Snow White got her, and we had one miss on circular logic.
Doc, Happy, Smelly, Sneezy, Stumpy, Sleepy, Grumpy, Dopey, Droopy, Bashful. Silly Bashful, if you were more assertive maybe you wouldn't have been pushed to the back of the line.
A) You only actually need a single weighing. You use one coin from the first box, two from the second, etc (N coins from the Nth box), weigh that pile and you'll find it is X/16ths light where X is the box number.
B) Three weighings are the minimum to guarantee you'll find it. Weigh a group of eight coins against another group, if it balances then the heavy coin is in the third set of eight, if the scale doesn't then the group that tips the scale has the heavier coin. We now have eight coins in which to find the counterfeit coin. Weigh three of these coins against another three of them, if it balances then only two coins remain, if it tips then once again, the group that tips the scale has the heavier coin. If only two coins remain then the third weighing is pretty straight forward. If three coins remain then pick two and compare them on the scale, if they balance it's the third coin, otherwise it's the one that tips the scale.
Five submissions, very respectable (especially when added to the 16 we got for BYOB Jr. for a grand total of 21!), Adam Weatherhead returns with a single correct answer, James Pearson gets 1.5, Chris Smith and the team of Brandon Wilkinson & Kevin Blair each get 2 right, but Joseph Bunyan wins with 2.5. So congrats Joseph, come on down to MC3038 (MathSoc Tetris Flashback Rehab Centre) to pick up your C&D gift certificate.
Despite the fact that it is the last issue, and I should be telling you not to submit, my role as dominator is too clearly cemented in my brain, so submit anyway! Not that I'll read it until sometime early May, but it'll make everyone in the world a little happier. Yes, that's right, everyone. Although tiebreakers aren't necessary (everyone is a winner when there is no prize), they'd still be lovely; after all, there will be problems in the first issue next term.
Instead of giving three problems, I'm going with one, because it's freaking long, and because it's one of those problems that is better done by walking away on occasion, so take your time, use it as a break from finals, use it to try to pick up, and get as many as you can (er, problems, I mean get as many problems as you can). If you get really stuck send me an email and I'll give a hint. So, without further ado, or with much ado about something:
A classic word game, you have to figure out what words the capital letters stand for.
Hope you enjoyed the Winter, may all your finals be easier than my column has been, see ya in the Spring term, when Slinkies rule the campus.
Snuggles "The Anti-Cheesus"