Who Finished In What Place?Date: 12/15/2002 at 20:12:33 From: Nicole Hoover Subject: Using problem-solving strategies Sarah, Carla, and Kim were the finalists at a gymnastics meet. Sarah was not second, and Carla was not third. Sarah's score was 0.6 point higher than that of the oldest finalist. In what order did the girls place in the gymnastics finals? I know Sarah was first or third place in the finals, with Carla being first or second. The line that is confusing to me is "Sarah's score was 0.6 point higher that that of the oldest finalist" since no age is stated for any of the finalists. I can't figure Kim's place in the gymnastics finals. I am sure that Sarah was in first place, with Carla in second place, and Kim in third place. Is that right? Date: 12/16/2002 at 12:29:18 From: Doctor Ian Subject: Re: Using problem-solving strategies Hi Nicole, To check your answer, I started by listing the places, and the girls who _could_ be in those places. Sarah wasn't second, so she could have been first or third: 1: Sarah 2: 3: Sarah Carla wasn't third, so she could have been first or second: 1: Sarah, Carla 2: Carla 3: Sarah Kim apparently could be anywhere: 1: Sarah, Carla, Kim 2: Carla, Kim 3: Sarah, Kim So what about this final clue? It's telling you that Sarah finished ahead of _someone_... which means she couldn't have been third: 1: Sarah, Carla, Kim 2: Carla, Kim 3: Kim And that eliminates all the possible orders but one. The key to working a problem like this is to be systematic. Otherwise you can drive yourself crazy. So what what does that mean, to be 'systematic'? Basically, you write down all the things that _could_ happen, and then you start looking for ways to rule out what _couldn't_ happen. And each time you rule something out, you go back and check to see if the change you just made rules something _else_ out. In this case, we just figured out that Kim must be third. That tells us she can't be first or second: 1: Sarah, Carla 2: Carla 3: Kim And this change makes it clear that Carla must be second, which tells us that she can't be first: 1: Sarah 2: Carla 3: Kim So I end up with the same answer you got. It's possible to make up problems that are _really_ complicated, like this one: Who Owns the Fish? (Einstein's Problem) http://mathforum.org/library/drmath/view/60971.html But if you'll look at the solution to Einstein's problem, you'll see it's just the same thing that we did here: Write down what _can_ be the case; eliminate what _can't_ be the case; and see if each change makes it possible to eliminate something else. As Sherlock Holmes observed, "When you have excluded the impossible, whatever remains, however improbable, must be the truth." That's the whole idea behind this kind of puzzle. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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