Number tricks at canvassing

Quick, think of a number. Multiply it by 2. Then, multiply the result by 5. Now, tell me the answer. There’s sure to be a zero at the end. I simply drop that zero, and I will know what your number was. Actually it will work with any number anyone can think of. Amazed?

Harriet Demetriou, Fernando Poe Jr.’s lawyer, tried to amaze voters with a number trick at Monday’s canvassing of the presidential tallies. It involved Certificate of Canvass No. 21, representing the votes counted in a local absentee voting center for election officials and deputized teachers, soldiers and policemen. Demetriou, a former judge and Comelec chief, proclaimed the CoC to be one of many that will prove massive, systematic cheating by the administration in the May 10 balloting.

Her numbers were simple. The CoC stated that the total number of ballots cast were 5,710. The five candidates got the following votes: Gloria Arroyo, 4,164; Panfilo Lacson, 988; Poe, 421; Raul Roco, 151; Eddie Villanueva, 102. Demetriou added the total votes for the five, and it came up to 5,826. Aha, it does not compute, she exclaimed. Arroyo must have cheated by 116 votes, because 5,826 minus 5,710 equals 116.

Demetriou presented a formula to "prove" her claim. She added all the votes for Lacson, Poe, Roco and Villanueva, and got 1,662. This should leave Arroyo with only 4,048 votes, assuming all the remaining votes went to her. But Arroyo’s tally clearly stated 4,164. Therefore, she must have been the one who cheated by 116 votes, because 4,164 minus 4,048 equals 116. And there are more such questionable CoCs, Demetriou concluded, predicting the figures in the ballot boxes yet to be opened. Arroyo is such a cheap cheat.

But wait a minute, wasn’t there a flaw in logic somewhere? Persons can beguile. But numbers are precise; we can’t fool around with them. In fact, using the Demetriou Formula, any one of the five could have cheated.

Here’s how it works. Let’s assume that Lacson was the cheat. It takes only a stentorian voice, uttered with authority, to say that at the Congress canvassing. Going by the Demetriou Formula, we add the votes of the four "cheated" candidates: 4,838. Lacson’s CoC tally was 988. Add his 988 to the four’s 4,838 and we get a total of 5,826 votes – versus only 5,710 ballots cast, or an excess of 116. Lacson must have cheated by that figure. Why? Look: 5,710 minus 4,838 equals 872 votes left. Assuming all the remaining votes went to Lacson, 872 should be his total. But he had 988. Let’s see now, 988 minus 872 equals 116. See? Lacson cheated.

But then, Arroyo and Lacson claim it’s Poe who did the cheating. They can prove it using the Demetriou Formula. First, add the votes of the four whom Poe cheated: 5,405. Subtract that from 5,710, and you get 305 votes left. Assuming all those votes went to Poe, he should have only 305 votes. But he tallied 421. Subtract 305 from 421, and we get 116 – the number of votes by which Poe cheated Arroyo and Lacson.

Let’s try it on Roco. Add the votes of the four whom he "cheated": 5,675. But there were only 5,710 votes cast, so 5,710 minus 5,675 equals 35 remaining votes. Assuming all those votes went to Roco, he would have 35. But the CoC stated that he tallied 151. See here: 151 minus 35 equals 116. Roco must have cheated by that same number.

In the realm of numbers, not the divine, even evangelist Villanueva could have cheated, using the Demetriou Formula. Add the votes of his mortal opponents: 5,724. Go on: 5,710 votes cast minus 5,724 equals -14. Assuming all those votes went to Villanueva, he should have negative 14. But the CoC said he tallied 102. Negative 14 minus 102 equals, really, 116. Hallelujah, brother, even Villanueva could have cheated.

Demetriou’s formula works with any number in the CoC. The fatal flaw of her logic was to knee-jerkedly claim there was cheating because of a discrepancy in the figures. And that it was Arroyo who cheated, when it could have been any one of the other four.

Or none of them.

Comelec lawyer Betty Pizaña was the vice chair of the canvassing committee for local absentee voters. It was she who entered the figure 5,710 in the CoC as the "actual number of ballots cast." She had made a mistake – an honest one, she says – which she already had explained during the Comelec’s earlier canvass of senatorial votes. That number came up back then when it appeared that several senatorial candidates, from both the Arroyo and Poe slates, tallied more than the stated number of ballots cast.

Pizaña says she reviewed her logbooks, and submitted a sworn amended report, stating that the actual number of votes cast was 5,923, not 5,710. With her corrected figure of 5,923, it would appear that 97 voters did not vote for president, since the total of the five candidates was only 5,826.

So much for that. Quick, think of your favorite number from 1 to 9, and I’ll give you an infinite row of that number. Wanna bet? First, multiply your number by 9. Remember the result. Now write down the numerals 1 to 9, but without the 8, as in 12345679. Multiply the result by 12345679, and you’ll get the row of your favorite number. It works anytime.

Try this one. You have a round rifle-target board of seven concentric circles. Each circle has a corresponding score if you hit it, namely, 11 for the outermost, 13 for the next circle, then 31, 33, 42, 44, and finally 46 for the bull’s eye. Question: what is the minimum number of hits necessary to score exactly 100 on this rather unusual rifle target?

If you answer "eight" hits, you can qualify for MENSA. The only way to total exactly 100 points is to hit 13 six times and 11 twice.

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