12/6/09
MacGyver Exercise: Math Without the Numbers
Tuesday, August 5, 2008When I first discovered that I can solve equations a little faster than the rest, I started questioning about half of the techniques taught in our school. I stopped following the processes and made my own shortcuts. They would fail me in my quizzes saying that I was didn’t follow what was taught. I always argued that I did follow the lesson, I just applied the concepts differently. Then I would challenge them to justify their methods, when mine does exactly the same but easier to imagine.
I kept on complaining about math teachers before who would make impossible exams. Examinations are supposed to measure your competency on a set of skills that were imparted. If this is what a teacher discussed, then this is what a teacher should expect the students to know. I’m all for making difficult exams (spoonfed tests are insulting) but I think before they give something that hard, it’s the teacher’s responsibility to equip us with the skills and discipline required to reach that level of critical thinking involved, don’t you think?
What pisses me off is that the very teachers who do not have that talent to imbue the analytical skill and discipline are the EXACT same a*holes who have the nerve to give a killer exam! To add insult to the injury, some even DELIGHT in seeing students fail…it’s their measure of how good they are. Will it be considered an assault if a student punches them in the face?
As expected, I became the teachers’ enemy. And it felt good. The beauty of mathematics is in its simplistic truth complying with Occam’s Razor– the final answer will be always the same no matter how many solutions one can come up with. And the simplest tends to be the best one.
I was so against unnecessary suffering. I always believed that math is supposed to make life easier (yes, easiER), and if life instead becomes complicated, then the purpose has just been defeated. The students are so preoccupied with the technicalities of problem solving that they lose focus on the heart of the problem: the logic behind the process–the “why-does-doing-this-solve-my problem” or “why-should-i-be-doing-this” concepts.
Of all the irony, that teachers’ enemy would become the very teacher. period. Well, partly because I was inspired by the good math teachers, partly because I want to prove to myself that I am NOT gonna be the teachers that I hated, but mostly because I find joy in teaching. This may sound cheesy but it brings me solace and a sense of peace to touch people’s lives with but the modest things that I can afford to share.
I’m no Math Whiz (okay may be a little but I’m no Einstein hell NO) but whenever I give out my lectures, I stress that Math is not about the numbers. It’s about the critical thinking of realizing the little things that you know, the things that you don’t know, and how you can exploit the little things that you know to unlock the things that you don’t.
I always remind them to spare themselves from unnecessary suffering. Lesson #1 is Huwag magpapakabayani dahil ang mga bayani ang unang… namamatay (Don’t try to be heroes because they’re the ones who get killed first) . There is a good reason why you need to remember dome formulae. Take advantage of that reason.
Math guys are pretty cocky with terms: “postulates” are just assumptions; “theorems” just mean shortcuts. “Corollaries” are just special cases. Why the f*ck should teachers ask students to memorize theorem 3.2 or corollary 12.17 aren’t they supposed to make students remember what those titles actually are all about?
I instill in my class my trade secret: the discipline that whenever I am taught a new lesson or faced with a problem, the first thing I ask myself is ALWAYS “So, if no one is there to teach me and no one’s going to tell me I’m wrong, how would I be able to figure out that this is what I’m supposed to do?” If you are able to answer this question, that means you are able to maximize your own limited resources and figured out a solution in a language that YOU understand.What follows cannot be THAT hard (though sometimes, shit happens so practice just the same)
On the last day of classes I give my students what I call the MacGyver Exercise. It’s a set of questions that can be solved by the same set of skills and discipline used to answer any math question, except that there are no numbers involved. I will give some of the questions, but I’ll leave the answers to you. I’ll let you know if I agree with your answer.
There are only a couple of rules–
You have all the money and wealth and resources in the world. Imagination is your limit. But let’s make things a little more juicy…
MacGyver (for the kids out there) is a TV series about the adventures of MacGyver (I forgot the firstname, it’s not Minemis FYI) who has the signature ability of getting himself out of any rough situation, no matter how crazy, by using every available resource within his reach. This means that he can concoct household cleansers to melt down locks while trapped inside a room or climb up a phone post to send morse code to seek help or something.
The first rule is to solve the problem using as little resources as possible. For as long as your answer satisfies the question, then your answer is correct. The question would be if there is a simpler way of solving the problem.
I am more interested on how you came up with your answers. So you must share how you figured it out. Don’t worry, I will not insult your answer. I have never made fun of my students’ effort to learn and I will not do it here either. Just try. 
But if you already heard the answer from someone else, don’t try to pretend that you figured it out. I will not know the difference, but you will. Pati ba to dadayain mo pa para lang masabing matalino ka? Konting EQ naman dyan…
Here goes:
1. How can you make a stick longer without adding (or subtracting) anything to is original length? ***WON BY Master joma***
2. A King has placed a large diamond at the center of a 50ft diameter carpet. How can you get the diamond without stepping on the carpet? ***WON BY Master Huxley***
3. Astronauts are having a problem while note-taking in space. Because of the lack of gravity, the ink will not go down the tip. How will you solve the problem? ***WON BY Master T***
These are just for kicks. Once I am satisfied with your answers, I’ll bring in the next batch. At your own risk.
Have fun. bwahaha
Previous Comments
@Huxley:
1. You can cut the stick lengthwise, the join the two halves together. If the stick is metallic, initin mo! hehe
**hmmm, this could work except that the problem asked for a way so that you don’t add to/subtract anything from its original length e. doing either preserves the mass, not the length. and that’s a clue for you! 
2. Pagpagin ung carpet until the diamond gets thrown off. Or you can just roll the carpet to, say about 24.5 feet then get the diamond.
**yea, this can work, provided that i have really strong muscles, so i’ll accept this.
** rolling the carpet was one of the real solutions here. this was what the royal janitor has done unconsciously after every one has given up trying. so, yes, this is a good solution! (2 points for you!)
** but i have a simpler way…
3. break the pen, then dip your fingers in the floating ink, then write notes with your finger(s)
** this is the first time i heard this answer! acceptable, but kinda messy. can you think of a simpler way?
–> Impressive, Master Huxley! Try answering these questions while intoxicated haha remember, I’m looking for a way taking the LEAST effort to solve the problem.
Posted by TBB at August 6, 2008, 6:13 am3. Use a pencil instead
Posted by T at August 7, 2008, 5:30 pm1. Lagyan mo ng s sa dulo. The word sticks is longer but you don’t necessarily change the length of the original stick.
Posted by T at August 7, 2008, 5:37 pm@T:
3. Use a pencil instead
–> yes, and this, according to the urban legend was how the cosmonauts dealt with the same problem. Being a genius doesn’t make you smart.
how can one solve when he does not know what he should be solving for?
one skill that a student needs to master is the ability to pinpoint what the REAL problem is amidst the confusion and how to attack swiftly. In this example, the problem is not the pen, but the situation. If the pen no longer serves its purpose, then find something that can.
Good job, T! 5 stars for you!
Posted by TBB at August 7, 2008, 9:54 pm@T:
1. Lagyan mo ng s sa dulo. The word sticks is longer but you don’t necessarily change the length of the original stick.
-> ay ang sarap bawiin ng stars. haha
imagine me showing meterstick. how do i solve the problem?
c’mon you can do better than that!
Posted by TBB at August 7, 2008, 9:56 pm1. Putulin mo yung stick then isaksak mo yung isa sa nagtanong dahil mas marami pang mas importanteng bagay na kailangang isipin like yung kakainin sa hapag kaysa ang sagutin ang mga kabalbalan na yan.
2. Hindi mo ba naisip na ipapapatay ka ng King kapag kinuha yon? Mas importante ang buhay ko sa diamond.
3. Makakahawak ka ba ng kahit anong bagay sa laki ng suot mo sa katawan bilang astronaut? I gow for my computer na silang dala for note-taking.
gusto ko yung answers ni huxley. i think he’s brilliant.
1. Putulin mo yung stick then isaksak mo yung isa sa nagtanong dahil mas marami pang mas importanteng bagay na kailangang isipin like yung kakainin sa hapag kaysa ang sagutin ang mga kabalbalan na yan.
–> then i guess you won’t have a problem answering something this “foolish”, now do you.
2. Hindi mo ba naisip na ipapapatay ka ng King kapag kinuha yon? Mas importante ang buhay ko sa diamond.
–> actually this is a story of a king who wanted to have a wise adviser and used this problem as a challenge. the reward for being able to do this is to become one of his advisers, plus he gets to keep the diamond. do you have a real answer?
3. Makakahawak ka ba ng kahit anong bagay sa laki ng suot mo sa katawan bilang astronaut? I gow for my computer na silang dala for note-taking.
–> now assuming that they are wearing the very thick spacesuits, as you say, i wonder how they will be able to press the keys with their large fingers just the same.
they won’t do note taking while outside the ship so they’re not wearing the space suits. computers aren’t very efficient for note taking because you will also need to draw diagrams along the way.
——
sarcasm comes with homework. nice effort, though, but you gotta do better than that if you really wanna piss me off.
Haha, mahirap pala pag masyadong pilosopo 
ahaha. seryoso ka pala masyado. sorry naman.
since 2 and 3 have been answered correctly already i’ll just try number one: let’s apply perceptual psychology. itapat mo yung dulo ng stick sa mirror. you’re not adding something naman on its length, it’s more on illusion.
Posted by joma at August 8, 2008, 10:45 am@T:
you weren’t the first to have answered that. the other answer from one of my students before was add i’s so it becomes stiiiiiiick. your answer and hers would have been great if only i was referring to the word, though.
i’ll give a clue.
what’s the difference of long, and longer?
@joma:
hmmm that could work except that you did an image to the length of the stick, so i’m afraid i can’t accept that yet. but your thinking is leading you very close.
for that, you deserve a clue:
CLUE#2:
go back to the basics. go back to the question. challenge the premise.
i have only one answer that i found acceptable so far. if you can only change your current train of thought (divert your focus from the mirror concept), you have no idea how close you are.:)
Posted by TBB at August 8, 2008, 11:00 ami don’t know. change your perspective on how you view the object?..maybe side view. arrgh.. i can’t think of any na.
Posted by joma at August 8, 2008, 11:16 ami’m having a problem with your question, make the thing longer or pwede ba to make it appear longer?
Posted by joma at August 8, 2008, 11:23 am@joma:
now THAT’s the right question to ask! you make it longer. now, answer me this
i didn’t say make the stick long, but make the stick longER. challenge the premise. wow i’m really impressed!
Posted by TBB at August 8, 2008, 11:53 amok, magtatabi ako ng mas maikling stick sa kanya.. now that stick is longer.
Posted by joma at August 8, 2008, 12:52 pm…and Master Joma owns #1!
will you be so kind to explain how you figured it out?
Posted by TBB at August 8, 2008, 12:56 pmp.s.
mukhang busy na busy ka sa trabaho mo no
haha..kelangan pa bang iexplain? maybe because of your clues.. and it’s in the comparative form kasi so dapat may point of comparison ka. ahaha. superr busy!
excellent.
what makes this so hard, is the premise on what that point of comparison is. when i said to make the stick longer, the question is, longer than..what?
but this question was neglected because we are already in the assumption that it’s supposed to be longer than itself (it’s original length, to be politically correct)
this also teaches us that some things affect us by just simply existing.
can you take some more?:P
Posted by TBB at August 8, 2008, 1:11 pmas promised, you’ll bring in the next batch. go!
** san na po ang next batch of challenging questions? **
Posted by joma at August 11, 2008, 10:40 pmwhoops sorry.
the next batch of questions will need diagrams and i’m too lazy to make ‘em.
i may be able to post the new questions by Friday.
Posted by TBB at August 11, 2008, 10:44 pmhahaha gapangin mo ung carpet tapos get the diamond ahahahha
Posted by jet at September 11, 2008, 12:29 ammy imagination tells me that:
1. i put the stick closer to my eye, it becomes longer.
2. if i roll the carpet till it gets half way, i can get the gem…i mean diamond.
3. and…if im the astronaut, i will just use a pencil. no nid for inks!
Posted by Mon at September 15, 2008, 7:58 pm@jet:
acceptable!
@mon:
1. i think the image may, but the stick won’t. if i measure it with a ruler near or far from your eye, it will give out the same reading. but that’s a good try!
2. rolling! it’s gonna be hard, it sure does the job!(read above comments)
3. couldn’t have said it any better myself. i’m sure if you had read this challenge any earlier, you would have beaten those who got the answers first.
@everyone:
i barely have time for myself during the past few weeks, let alone do the diagram for the next batch of questions. i’ll give an update once i posted the next batch. thanks for bearing with me
Re: #2:
Ngayon ko lang nakita ‘to, but i guess you can cut the carpet as you move towards the center, so you can avoid stepping on it or having to roll it.
Posted by jackass at October 31, 2008, 2:38 pm@master jackass:
Yes, this is an easier answer, since it will take less muscle power to finish the job. actually, one condition forbids the use of any instrument, but i forgot to put it in, so i’ll accept your answer. you got me there, man!
***this is the last time that any other external object will be allowed: all succeeding solutions are forbidden to use any instrument***
Posted by TBB at October 31, 2008, 7:47 pm1. give the stick something smaller to compare it with. kappish, it becomes longer. sabi nga sa previous comments its a matter of comparing lang (pero i would look like i copied his answer hahahaha, pero i didn’t, though.)
2. rolling the carpet would be easier, if you ask me. if you cut the carpet towards the center, then you’ll still be using muscle power to pull it away as you need space to walk on towards the center and get the gem. furthermore, its a carpet, plus its not just a carpet, its a persian carpet (right?) imagine cutting something that thick even if you’re using big sharp scissors
3. ive seen in Nat Geo a few years ago that astronauts use pencils to write their data, and so does deep sea divers. pero nasagot na din to.
may winners na, so this is completely pointless and unnecessary, but ill post it anyway. hehehe
bring out the new batch TBB!
Posted by michael at November 1, 2008, 2:31 pmi think cutting it is easier relative to the weight of the carpet that you are trying to push, but yes, you may also be right.
no, of course it’s not pointless because..uhmmm..i..uhm personally believe that..uhmm..ok yeah, it’s pointless haha
seriously, your answers will be pointless, if you’re here just for the win. otherwise, you’re cool.
Posted by TBB at November 1, 2008, 2:48 pmokay, which would you prefer? body aches (relieved by analgesics within minutes) for trying to roll the carpet or second degree blisters (pain not relieved by simple analgesics and remains painful for a couple of days) on your fingers for trying to cut the carpet towards the gem?
i’d go for the former. hehehe.
and oh yeah, this site is cool. are you from UP?
Posted by michael at November 4, 2008, 3:23 amthat will depend on the scissors.
If I wasn’t from UP, would it have made a difference?Wait, don’t answer that–the last one who did got one hell of a beating.
please read the entry And The Bitter Bastard That Was.
Posted by bitterbastard at November 4, 2008, 7:21 amnatakot ako bigla. wahahaha.
Posted by michael at November 4, 2008, 3:22 pmgood.
1.)itatapat ko ang stick sa ilaw…hehehe..considered naman yung shadow dibah(halatang lasing ba?)
2.)gagamit ng tali(d maxado halata na mahilig sa spy movies)
3.)use computers or recorders,cameras and etc…
this is my answers to your questions..though already answered correctly by the other people…i prefer giving my answer..why?eh gantio ako mag-isip eh..hehehe…
Posted by paul_devil at April 6, 2009, 2:38 pm
Hula hula lang
1. You can cut the stick lengthwise, the join the two halves together. If the stick is metallic, initin mo! hehe
2. Pagpagin ung carpet until the diamond gets thrown off. Or you can just roll the carpet to, say about 24.5 feet then get the diamond.
3. break the pen, then dip your fingers in the floating ink, then write notes with your finger(s)
Posted by Huxley at August 6, 2008, 12:05 am