How good are you at guessing?

May I share this one.

A page of a newspaper is not very thick, about 0.003 inch (in.), and you often have seen a stack of newspapers. Suppose you were to place one sheet of newspaper on the floor. Next you place another sheet on top of the first, then two more sheets, then four, and so on, building up a pile of newspaper. [COLOR=Indigo]Each time you add to the pile as many sheets as are already there. After the tenth time you would have a pile about 3 in. high. If you were able to continue until you had added to the pile for the fiftieth time, how high would the pile be?[/COLOR]

One of the answers (a) through (d) below is the correct one. All you have to do is guess, or calculate, which one it is.

a. About as high as the standard table.
b. About as high as a four-story building.
c. About as high as the Empire State Building.
d. More than twice as high as the Empire State Building.

Just make a choice...

🙄

I'll just tell you what it is later.

a

D.

I think it has to do with 2^15 power, so twice the empire state building

Um... B?

..or you may reason out why... 😎
a sort of personal analysis. 😉

I usually love math, but I thought this was a guessing game. 🤨

I think it has to do with 3^15 power, so empire state building

❌ nope

I'm still with B... Though I am very dumb, I'm sticking with my foirst answer. I'm just like that.

I usually love math, but I thought this was a guessing game.

I have it ... its .003 X 2^N N equal to the number of times
so .003x2^15 which is about 98.304 inches or 8.2 feet

d

25 or 15 more times would be 8388.6 feet or 2 empire states

I have it ... its .003 X 2^N N equal to the number of times
so .003x2^15 which is about 98.304 inches or 8.2 feet

no It grows exponentially.
I did somethign like this with pennies once. It was a problem like if you got paid 1 penny one day and then it doubled the next day and the next and so on and so forth and at the end of a month you had over a million dollars so its the same thing.

no It grows exponentially.
I did somethign like this with pennies once. It was a problem like if you got paid 1 penny one day and then it doubled the next day and the next and so on and so forth and at the end of a month you had over a million dollars so its the same thing.

✅ uhuh 🙄

Tell me when you get the answer.

I have it ... its .003 X 2^N N equal to the number of times
so .003x2^15 which is about 98.304 inches or 8.2 feet

Well...?

okay... I'll end it now...

This is one of many fairly common situations in which mathematical analysis helps you discover amazing facts that would not occur to you in any other way. The discovery aspect of mathematics is as prevalent and as important as its use in problem solving.

Here’s the answer:

Since each time you add to the pile you are doubling the number of newspaper pages,
after 50 times you would have “2 raised to the 50th power” sheets.
A table of powers of 2, or straightforward arithmetic, will convince you that you would have 1,125,899,906,842,624 sheets.
A little more arithmetic will indicate that the pile would be well over 53 million miles high;

[COLOR=Red]that is, more than one-half the distance from the earth to the sun. 😱 😄

It goes something like this:

Initially,
2E0 = 1 sheet
Then,
2E1 = 2 sheets
2E2 = 4 sheets …
2E50 = 1,125,899,906,842,624 sheets

Therefore,

1,125,899,906,842,624 sheets x 0.003 in./sheet = 3,377,699,720,527.872 in,

or 53,309,654.68 miles[/COLOR]

Even if you reasoned that (d) was the right choice, you probably did not realize it represented so much of an understatement.

Good job everyone 😎

That's why I love mathematics.

Thanks for dropping by. 😎