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.