How many 2's?

Here's a 1 question quiz for you:
As a fraction, what portion of the whole numbers 1 through 100, inclusive, contain the number 2?

The answer is later in this post.

This math question has stuck with me ever since 8th grade.  I missed that question in a math skills competition called MATHCOUNTS.

The reason I mention MATHCOUNTS is that my team at the office will be volunteering as graders at the local competition here in Des Moines next week.

That's right, it's my time to come full circle and give back to the competition that I competed in when I was younger.  It's basically a few math nerds from each middle school gathering together to see who is the nerdiest.  I guess it is time to admit to my nerdism.  I won my local competition and earned the right to compete in the state competition.  I point this out not to brag - I mean who really brags about a competition in 8th grade when they are 31? - but as a means to point out a dichotomy later.

The state competition was at Drake University in Des Moines, so we had to travel for three hours just to compete.   The way it works is that you get a certain number of rounds of individual and group rounds where you are just sitting at your individual desks.  It looks similar to a college classroom where 200 people are all taking their final exams at once.  The only thing you had to worry about was getting the answers correct for the current round.

Then there is a break for all of the graders to get done scoring each of the rounds.  Once the scores are tallied they announce the top ten competitors.  I was announced as the one in 6th place.  I remember thinking to myself, “This is awesome!”  I wasn’t expecting to do as well as I did.

This is not our final placing.  We then start a challenge round for final placement.  The challenge is a best of 3 questions (or 5? I can’t remember) going head to head with a competitor.  First, the 10th and 9th place competitors square off.  The loser of the challenge gets 10th place, the winner gets to challenge 8th place.  So they then battle and the loser gets 9th place, etc.

The first couple of rounds occur and the 10th place initial finisher won his or her first couple rounds but gets beaten by the person initially in 7th.  It is then my turn.  I take my seat at the competition table for my battle.  The first person to buzz in with the correct answer wins each point.  If you answer and are wrong you are not allowed to buzz in again for that question.  Your opponent can then take the rest of the time allotted for each question.

I don’t remember what the questions were other than the one above.  I do remember that my opponent was in a hurry for the first question and got it wrong, giving me time to methodically get the correct answer.

Answer to the quiz from above: 19 / 100 [2, 12, 22, ... 92, and 20 - 29, each sets of 10, but remember to subtract one to account for the double counted 22]

The second question was the quiz question.  I remember arriving at the number 19 quickly.  I went to buzz in, and was acknowledged without much hesitation.  Somewhere between when I sounded my loud buzzer and when the words began coming out of my mouth the nerves got to me.  Somehow 19 got placed in the denominator and what ended up coming out of my mouth was “one-nineteenth”.

I don’t remember the exact proceedings after that, but I do know that the final score was either 3-2 or 2-1.  I lost my battle because of that one question.  That meant that I ended up in 7th place.

The boy who beat me ended up making it all of the way to 4th or something.  After my loss I was doing the problems at the same time as the competitors just to see how I could have done.  I had the possibility of getting as high as third.

But I didn’t place that high.  My nerdy math smarts didn’t do me a bit of good since I couldn’t transform my hasty chicken scratches into a reasonable short oral answer.  I did learn a thing or two about myself that day.  I learned that I have times when I do not perform well while under pressure.  That lesson has been reinforced numerous times throughout the years.  Apparently I am not a lump of coal that can be pressured into a fine diamond.  This is probably similar to why I would be a terrible car salesman or some other high pressure sales job.  Yucchhh.