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Hi;

What does the book think of this one?

I'd like to see a version where he really explains everything critically from an expert's point of view.

Hmmm, so we should ignore what he does say in favor of what he does not?

I didn't watch the video, but I heard all of it.

Then it would seem your ears are smarter than your eyes.

Hi;

There are a couple of ways to approach this type of problem. The best ones are computational but I suppose it can be done the classical way too.

Looks like you can break the shape up into 4 right triangles. Please try that and let me know how you do.

Hi;

Did you watch the video? I think the point is whatever them there fellows are doing, he does not like it. Pay close attention to the comments around 5:45. Remember L's comments about human mathematics? Looks like, ole Wolfy has been to Nevada and not just Vegas either.

Then we are done?

Here is how to prove it computationally, you see that M knows it is impossible.

This may take a while to finish.

```
FindInstance[{a1*b1 == 1/11, (a2*b1 + a1*b2) == 1/
11, (a3*b1 + a2*b2 + a1*b3) == 1/
11 , (a4*b1 + a3*b2 + a2*b3 + a1*b4) == 1/
11, (a5*b1 + a4*b2 + a3*b3 + a2*b4 + a1*b5) == 1/
11, (a6*b1 + a5*b2 + a4*b3 + a3*b4 + a2*b5 + a1*b6) == 1/
11, (a6*b2 + a5*b3 + a4*b4 + a3*b5 + a2*b6) == 1/
11, (a6*b3 + a5*b4 + a4*b5 + a3*b6) == 1/
11, (a6*b4 + a5*b5 + a4*b6) == 1/11, (a6*b5 + a5*b6) == 1/11,
a6*b6 == 1/11, 1 > a1 >= a2 >= a3 >= a4 >= a5 >= a6 >= 0,
1 > b1 >= b2 >= b3 >= b4 >= b5 >= b6 > 0,
a1 + a2 + a3 + a4 + a5 + a6 == 1,
b1 + b2 + b3 + b4 + b5 + b6 == 1}, {a1, a2, a3, a4, a5, a6, b1, b2,
b3, b4, b5, b6}, Reals]
```

That is correct.

The column is called billions and it is the next one after hundreds of millions. What funny names these columns have... Imagine going through life called "hundreds of millions." Boss to "hundreds of millions," if you are late one more time "hundreds of millions," I am going to can you like a tuna.

1,234,567,890 This one will be harder. Just remember the names of the columns and you will get it.

245678931

The next column is the hundreds of millions column, so how is 245,678,931 pronounced?

Yep! Remember you do not usually have to deal with numbers that are much bigger than that. For instance:

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

Speaking that out loud would just not be practical.

That is very good. If you have some spare time go here:

http://www.mathsisfun.com/place-value.html

What can we do now?

Very good, here are the names of the columns all the way to the millions:

Can you do 4567893 now?

Correct!

That shows the names of the first 3 columns.

Supposing our poor guy owes the bank $7893 on his mortgage, how do you say that?

That is correct! And if he has a car payment this month of $369?

Let us try something. A guy's power bill is $279. How do you write that in words?

Grouping in three is fine, I am just showing you where the names of the columns come from.

4567893

The eight is in the hundreds column and the 7 is in the thousands column. Okay?

4567893

The first number on the right is the units or ones digits, the second from the right (9) is the tens digit. Okay, so far?