Start spelling each word as you count, starting with one.

How high do you have to count before you reach a number that has the letter "a" in it?

Counting each number 'correctly,' and counting only whole numbers, as is implied but not stated in the problem, you have to count to "one thousand," since 100 is "one hundred," not "a hundred," and 101 is "one hundred one," not "a hundred and one."

If you count in increments of anything other than an integer (still assuming only rational numbers), the next number you say will have the word "and" in it, since that is the correct way to pronounce it (ie, "one and one third" or "four and three eights").

The only exceptions there would be if you are counting backwards (or by a negative number). Then, the next fractional number you say may be between zero and one (ie, two thirds), and may not have an 'a' in it. Once you are below zero, any number will work since you say the word "negative" before each value (one, zero, negative one, negative two. . .). Since the problem does specify "how high," that can probably be ruled out.

Regardless, the immediate and technical answers are the same: one thousand.

Posted by DJ on 2003-04-24 19:16:20