Logic.

One of my classes is supposed to be about elements of geometry. Instead, we have a middle school geometry textbook, which we are working through as if we are actual middle schoolers. It's not what I expected from a college level Mathematics Education course. Aynways, the other day the teacher gave us a homework handout, which actually wasn't even about geometry. It was about reasoning and logic and such.

Logic is something that we learn all in school that doesn't really apply too often in real life. It happens in school and in fictional media. For example, when Harry and Hermione, in the first Harry Potter book, are in the one room of the potions with the poem that Hermione uses logic to figure out ("Most wizards don't have an ounce of logic," she says. Those wizards obviously never took middle school geometry.) Also, in the movie Labyrinth, from sometime in the '80s, the girl gets to two doors, each with a gaurd, and is informed that one gaurd always lies and one always tells the truth. Good thing she had logic skills that mysteriously appear for this one scene alone!

Now, here is one of our logic problems:

"Five identical sweatshirts are placed in a bag. A letter is stitched to the back of each shirt; two of the letters are L's and three are W's. Chris, Hugo, and Mary each pull out a shirt without looking at it and put it on. Chris can see Mary's and Hugo's shirts and correctly deduces, "I cannot tell which letter I have on." Mary sees only Hugo's shirt and draws the same valid conclusion. Hugo sees no one's shurt but uses his logic and is able to tell whch letter is on his back. How does Hugo do it?"

Now. This is in no way a realistic situation. This course is from a fancy new-age textbook. The newer math philosophies focus on math being applicable to real-life. Then the students will be interested. Now, when is this applicable to real life? Here are some of the errors with this problem:

1. Why are the letters stitched on the back? And why 2 L's and 3 W's?
2. Are the three peopel standing in a line and refusing to look in any other direction?
3. Why did Chris and Mary decide to deduce such things?
4. Why didn't they look at the shirts before they put them on?
5. From where did the shirts come?
6. I've never met anyone named Hugo.

These are just some of the many unrealistic things in this problem. Now, SPOILER ALERT. This is how the middle schoolers are supposed to solve this problem, by which the majority of my class was baffled.

First, assume that when Chris and Mary deduce, they do so out loud. When Chris deduces that he cannot see his letter, we know possible options for Mary and Hugo. They are: A.) Mary and Hugo each have a W, or B.) Mary and Hugo have one L and one W between the two of them. This is becuase if they both had an L, since there were only two L's, Chris would have known he had a W. Now, Mary, being bright and educated, heard Chris and realizes that she and Hugo do not have two L's. So she sees his shirt, but cannot make a conclusion. THIS means that Hugo must have a W. If Hugo had an L, Mary would have known she had a W, since they cannot both have an L. However, if Hugo has a W, Mary can have either an L or a W since both of those options leave Chris clueless. Hugo, hearing Mary, knows that he must have a W.

While I find this problem somewhat fun to work out, I also find it a little pointless. Does it matter if Hugo knows that he has a W? Does anyone care? Highly doubtful. Students will read this problem and think, "Logic is stupid. If this is all it's used for, then I don't care to have any."

This is a better version of the above problem.

"Five identical sweatshirts are placed in a bag at a tournament where the grand prize is $100,000 and an A on a math test for figuring out what letter is on the shirt. A letter is stitched to the back of each shirt; two of the letters are L's and three are W's. Chris, Hugo, and Mary are the contestents. They were chosen because of their supreme logic skills; however, the Olsen twins are attending the tournament and have bet against all of them, especially Hugo because of his rarely used name. Each pull out a shirt without looking at it and put it on, then stand in a line, since those are the arbitrary rules. Chris can see Mary's and Hugo's shirts and correctly deduces, "I cannot tell which letter I have on." Chris, being correct in his deduction, is not killed. Mary sees only Hugo's shirt and draws the same valid conclusion. Her conclusion also spares her life, while not winning her money or good grades. Hugo sees no one's shirt but uses his logic and is able to tell whch letter is on his back. He wins the prize and dissapoints the Olsen twins, while sparing his life. How does Hugo do it?"

This scenario will get the attention of students much more easily than the before problem. Lives are in danger, celebrities are involved, there is money, there are grades. The students can relate this to themselves. What's more, now it all makes sense as to why these three people are doing what they do. And there's incentive for students to use logic! Much preferable than the problem before.

But even if it wasn't, logic still really doesn't come up much in real life unless you happen to be in some odd life-threatening situation with a logic puzzle for an answer. Back to Labyrinth, the girl was at two doors. One guard always lies, and one always tells the truth. She is allowed to ask one yes-or-no question to one guard. One door leads her correctly, one door leads to death. She somehow decides to ask a question to one guard that is something like, "If I asked him if his door was right, what would he say?" This question confuses even the guard, who responds hesitantly, "Yes?" (He might have said no, it's been awhile, but it's the same logic.) This smart teenage girl now knows which door. If she were talking to the lying guard, then he said yes when the truthful guard really would have said no, he guarded the wrong door. If she was talking to the truthful guard, then the answer was yes, it was just that the lying guard would say yes, that his door was right when it was STILL the wrong door. Either way, the guard she asked is guarding the correct door!

I guess the moral of the story is to learn logic, because you never know what adventures in life require logic to save your life.