1. ## Problem Four

Problem Four

No Ones

I programmed my computer to print the integers from 1 to 1 000 000. However, my printer was defective and printed a square instead of the numeral 1. For example, 2191 was printed as 2[]9[].

1. Immediately after the integer 100 (that is []00) had been printed

a) How many squares were printed altogether?
b) How many of the 100 integers was printed correctly? Explain.

2. How many of the 1 000 000 integers printed were printed correctly? Explain.

3. My printer normally prints 100 digits per second. Since it takes longer to print a square than a digit, in its defective state my printer took 2.13 seconds to print the first 100 integers.

How long did it take to print a square? Explain.

2. Hello, MrFantasy!

Here's the first part . . .

.: Problem Four :.
No Ones

I programmed my computer to print the integers from 1 to 1,000,000.
However, my printer was defective and printed a square instead of the numeral 1.
For example, $\displaystyle 2191$ was printed as $\displaystyle 2\square 9\square$

1. Immediately after the integer 100 (that is $\displaystyle \square00$) had been printed,

a) How many squares were printed altogether?

. . $\displaystyle \begin{array}{ccc}\text{Decade} & \text{No. squares} \\ 0-9 & 1 \\ 10-19 & 11 & {\color{red}*}\\ 20-29 & 1 \\ 30-39 & 1 \\ \vdots & \vdots \\ 90-99 & 1 \\ 100 & 1\end{array}$

* .20 numbers were altered, but there were 21 squares.

b) How many of the 100 integers was printed correctly? Explain.
As noted in part (a), 20 numbers were altered.
Therefore, 80 were printed correctly.

3. Mmmm, that is correct. But I still coudn't see the pattern. I mean 11 has 2 squares because there is 10 , 11 , 12, 13,14 etc.

So this would occour everytime when starting a new hundred. But how can you put this into a formular, then with forumlar we can then work out how many of the 1 000 000 integers printed were printed correctly.

Am I right?

But for part 3, I still coudn't figure out. I am gonna try it late, laters.

MrFantasy