יום חמישי, 17 במרץ 2016

Oranges and Apples

On my last post we talked about getting interesting information from even site like IMDB.
This showed us a bit on how easy it is to learn thing when they are easy interesting and fun.

"You become better at it and it becomes more fun..."

Now you probably all know the saying "Use it or Lose it". 
Personally I don't like when someone is trying to move me to action by scarring me. But there is a point here.
If we have some ability but we don't practice it, with time we would lose this ability. But the good thing is, that the more you do things, they become easier to do, you become better at it and it becomes more fun.

Driving or riding bikes is a good example, but same thing is true even for using math.
So I want you to feel good about yourself, so lets start with some easy math questions.

For example, you have 2 oranges and I give you 2 more. How many oranges do you now have?

What if you had 2 apples and I gave you 2 more, how many apples would you have?

2 Bananas + 2?


"Ones you know how to add numbers you can add anything..."

You get the idea, so continuing with this question will make you board. But what is important is that ones you know how to add numbers you can add anything, fruits, cars, people, at the end of the day adding is numbers.

So now that you know everything you can learn from these 2+2 questions, I have another question, and this is a logic question, and again - its about fruits.



You have 3 closed boxes of fruits, one has oranges, one has apples, and one has oranges and apples. You don't know what is in each box, and to make the matters even worst, though each box has a label that is suppose to say what it has inside, you know that the person who  put those labels is a pathological liar who always lies, so you can't trust any of the labels.

But you know what, since I'm such a nice guy, I will let you select one of the boxes, and pull out one fruit.
But after doing that, I expect you know what fruits are in each of the boxes.

So - thinking time...

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"Words can be confusing..."

This is an easy one, and you probably solved it, but don't beat your self if you didn't. This is not a test, and we are not here to get everything right and pump our ego. We are here to learn something interesting.

The first thing you should know, that a lot of times in life, words can be confusing. For example I said 
"and to make the matters even worst, though each box has a label that is suppose to say what it has inside"

It's not really worst. Actually if we didn't have labels, we wouldn't know where to start.

Next I say "the person who  put those labels is a pathological liar" 

Usually we think of lying as a bad thing, and a pathological liar is someone you can't ever trust. But actually someone who always lies, is better for us than someone that lie part of the time. If someone always lies you can ask him true or false questions, and what ever he answered you you know that the opposite answer is the right answer.


In our case, if a label says that there are oranges in the box, we know that this box does not contains only oranges. It either has apples, or apples and oranges. And because we know all the labels are false it is true for any box.
So the box that has label that says apples, has either oranges or apples and oranges. 
Now what about the one that says oranges and apples? Well - we know for a fact that it has either apples or oranges. So... if we pick a fruit from this box we know what insides, it would be either oranges or apples. 

Lets say we found an apple, then we have to more boxes. one has oranges and one oranges and apples. But the oranges labeled box can't really hold oranges, because if that was the case then the label on that box was not false, and  we know it has to be false. So the box that says apples would have oranges and the box that would say oranges would have both apples and oranges.

Almost the same happens if we found orange in the box labeled apples and oranges.

So - this is all nice. We learned that when we know something is a lie it tells us about what is true, but what else? 

"If you are looking for additional interesting data, many time it is best to look at what is different, what is exceptional"

We also might notice that as in the 2+2 exercises, we could change the question to have pineapples and bananas , or baseballs and tennis balls and the solution would still be the same. But what else?

Well, after solving this question you might have noticed another thing. Not all boxes are the same. 
What do I mean? Well - in a way the box labeled oranges and the box labeled apples are the same. Both gives us the same type of information. But the box labeled oranges and apples is different, it has other information type. So if you think about it, it makes sense to check the box labeled oranges and apples first, because we can expect that the other two would give us somewhat different information. 
This is an important observation, if you are looking for additional interesting data, many time it is best to look at what is different, what is exceptional. 

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Are you feeling smarter already? I do.

We took a look on some important ideas on how to learn from a question, even if we don't solve it. 
In one of the next posts we would take closer look on how our perception on question and challenges can change our learning skill dramatically. And make learning even more fun.



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