The license plate game Or something to think about while caught in traffic

One activity I entertained myself with as I was growing up was looking at vehicular license plates. Sitting through a traffic jam, I would look at a license plate’s last three digits and, oblivious to my parents’ complaints about the traffic, happily spin numbers in my head. It made me an ideal passenger, always quiet and content.

At that time, plate numbers were still of the "letter-digit, digit-digit-digit" combination. Sometime in my teen years the license plate combinations changed to "letter-letter-letter, digit-digit-digit." Not bothering then with the reasons for the change, I expanded my number game to trying to count the total number of three-letter combinations.

As my study of mathematics deepened (meaning, as I learned how to count properly mathematically), I realized that the change from the five-character combination to the six-character one implied a huge increase in possible vehicle registration, and that traffic jams that would ensue would be just as huge! Now I no longer wonder why traffic jams are inevitable, especially in Metro Manila. This would give my parents, and all commuters, more to complain about.

Let us dissect the present license plate configurations, and concentrate on those from Metro Manila, a.k.a. the National Capital Region (NCR). First, let us look at the first three figures: the three letters. To make computation less complicated, I will fix the first letter, say, N. NCR license plates originally began with N, with the exception of course of government vehicles or "red" plates which start with S, and other special registration plates. (Region I license plates begin with A, Region II license plates with B, Region III license plates with C, and so on.) Next, we note that the letters I, O and Q are never used in license plates. That means that the second and third letters may be any of the 23 remaining letters of the alphabet (letter repetition is allowed). Rules of counting dictate that the total number of three-letter combinations with the above restrictions is 1x23x23 or 529.

Next we look at the last three figures: a three-digit number. This automatically bars 0 as the first digit. However, repetition is allowed so the total number of three-digit numbers is 9x10x10 or 900. (We may avoid the hard math for this by just figuring out how many numbers there are from 100 to 999.)

Again, counting rules dictate that if we want the total number of six-figure combinations with all the above restrictions, that is, three letters where the first one is N and a three-digit number, then the total number of such license plates is 529 x 900 or 476,100.

I am sure you are aware that license plates in the region have gone through several different first letters already, namely, N, P, T, U and W. When I began writing this article new license plates still started with X. Now, I am seeing plates starting with Z! This means that vehicle registration in NCR has used up 6 x 476,100 or 2,856,600 license plates! This translates to 4,560 vehicles per square kilometer of Metro Manila’s 636 square kilometers. As I noted earlier, this still excludes government "red" plates, customized/personalized plates that start with letters other than N, P, S, T, U, W and X, and possibly diplomatic "blue" plates that follow an entirely different configuration.

Fortunately for our health and travel concerns, theory and actual fact differ significantly. Not all of these almost three million vehicles are in use. I expect that quite a number have found their way to different endings – some sitting and rotting away in streets, garages and junkshops, some impounded, some "chop-chopped." Then there is the DOTC directive implemented last year wherein jeepneys and buses aged 15 years and older can no longer have their franchises renewed. Hooray! I hope the implementation has been successful. In any case, the DOTC-LTFRB website says that the actual number of registered motor vehicles in Metro Manila, as of Sept. 30, 2004, was just 852,045 (32 percent of total motor vehicle registration for the entire country). I say "just 852,045" relative to my initial estimate of almost three million vehicles. Then again, this is on the assumption that all vehicles have been properly registered. Still and all, 852,045 is as big as it looks and sounds.

Imagining 852,045 vehicles moving around in a space that is roughly only 636 square kilometers overwhelms me. Metro Manila covers only 0.2 percent of the Philippines’ total land area, yet it is home to almost one-third of all motor vehicles in the country. Sadly, this is not imagination. This is for real. The DOTC-LTFRB figures translate to 1,339 vehicles per square kilometer! Now should we wonder why we have perennial traffic jams and worsening pollution? Why MMDA is continually cooking up schemes such as color-coding? The color-coding scheme aims to reduce vehicular traffic by 20 percent. This 20 percent already means 170,409 vehicles; but a whopping 681,636 remain! Moreover, even with the number of flyovers and fly-unders being constructed, traffic still does not "fly" through these thoroughfares. Though they are welcome attempts at easing traffic flow, most usually turn out to be "crawl-overs" and "crawl-unders." The biggest culprit is sheer vehicle volume. Perhaps the government should also look for schemes of regulating vehicle registration instead of easing traffic flow, which is near impossible if registration is unlimited within a very limited land area.

Check out, if you can, vehicle registration in the other regions. Has Region I used up its A-plates, Region II its B-plates, Region III its C-plates, and so on? If they have not, then lucky are their citizens. While in NCR, by the time we use up our Z-plates,…

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The author is an associate professor of Mathematics in UP Diliman. Her research areas include partial differential equations and operations research. A current interest is General Education Mathematics which she has been teaching for the past several semesters. E-mail her at [email protected]