There were some numbers on the page, also, and I wondered if they were a key to the code. However, they looked like a telephone number: seven digits, with a dash between the third and fourth digit, and after trying for a few minutes to connect them with the code in some way, I gave up and decided they were what they appeared to be.
After several hours I had achieved exactly nothing. I took a break for lunch and then decided to give my brain a change of pace by attempting to solve Mark's oddball problem. Twelve balls, balance scale, one ball heavier or lighter, three weighings. That should be simple for me.
At first I floundered. If I weighed six balls against six, one side would be lighter. So what? I knew that already. And I knew from experience that problems like this couldn't be solved with straight-line logic.
By trial and error I approached the solution. Split the 12 balls into three groups of four. Weigh group A against group B. If they balance, the oddball is in group C, so all but four balls have been eliminated. Otherwise, it is in group A or B but its relative weight will be known when it is found.
So far so good. Now came the tricky part. Assuming the oddball was in group A or B, the second weighing demanded creative thinking. With a balance scale one tended to think in even numbers, but I discovered that this didn't work. I had to remove three balls from the second weighing, for example one from group A and two from group B. I replaced one of the removed Group B balls with a Group C ball to keep the same number of balls on each side of the balance scale.
Once I hit on this approach the solution came quickly. I wrote it out in all its ramifications to show to Mark. And to prove I wasn't yet senile. Invigorated, I returned to Carol's code. Perhaps straight-line thinking wouldn't work in solving this, either. I assumed that she was writing in English, but what if she wasn't?
The only language I could think of that might contain as few as ten letters in a typical piece of text was Hawaiian, which has place names like Aiea, but I doubted that Carol knew the Hawaiian language.
What if it wasn't a language at all? What if it was…numbers? Of course! We use a base-ten number system, which means that there are ten digits. Why? Probably because we have ten fingers and ten toes. Each of Carol's ten letters must represent a digit, from 0 to 9. The fact that the letters were lined up in nice neat columns lent credence to this argument.
My euphoria didn't last long. Even if I was right, even if I could assign a digit to each letter, what would it mean? I did make an attempt to assign digits to letters. Maybe one column was composed of dates. No-there weren't the regular patterns of numbers necessary for days, months and years.
I did discover two patterns. The numbers (I now assumed they were numbers) in the third column started with just three different letters, but in no particular order. And the numbers in the first column started with just two different letters.
The first four numbers in the first column started with P and the other six started with S. Although this column might consist of numbers in sequence, they definitely weren't consecutive. Based on the sequential assumption, I could probably determine that some letters represented digits higher than others. For example, S was probably one higher than P. But by this time I was tired of the whole thing.
Well, Lillian, I thought, you've had your fun. Maybe now it's time to get on with the business of living. Whatever that meant. The first thing I did was to phone Tess to find out how the water aerobics class had gone. At least that was my excuse.
“What have you been doing with yourself?” Tess asked.
I told her. When I mentioned I had solved the oddball puzzle, she said, “Well, at least you don't have Alzheimer's.”
“That's comforting to know.”
“By the way, you left Silver Acres just in time. All us inmates received notices in our mailboxes today saying that our monthly fees need to be raised by two percent.”
“They just raised the monthly fees in January. And there's only supposed to be one increase a year.”
“Right. Which is why we have to vote on this one. There's going to be a general meeting tonight to acquaint us with the reasons for it. But you should be proud of me. I'm not taking this lying down. I've already called Wesley, our gallant leader, and complained to him.”
“And what did Wesley say?”
“He said that Carol advised him of the necessity for the increase on Friday. Like the good accountant that he is, he asked to see the books. Carol said fine and put him in touch with her bookkeeper. So he is in the process of looking them over.”
It wasn't a bad idea to have a CPA as president of the residents' association. After I said goodbye to Tess, I called Wesley on a hunch.
After our hellos, he said, “I was shocked when Tess told me you have been evicted from Silver Acres. I'm looking into it. I suspect it was unjustified, in which case I'm going to get you back in. In fact, I wish you had come to me before you agreed to leave.”
I'd never thought of that. I guess I had been in a state of shock, myself, especially since Albert had a part in the plot. I thanked Wesley for his help but mentioned that my apartment was probably already taken.
“No, it isn't,” Wesley said. “I made Carol promise to hold it open until I have a chance to investigate. I may take this to the board.”
Good old Wesley. After thanking him again I said, “I understand that you're also looking at the books of Silver Acres because of the proposed increase in fees.” When he acknowledged that he was, I said, “I just may have some information pertinent to that. I can't talk about it on the phone. Are you available tomorrow morning?”
“I'll make myself available because this is important. And I'll know more in the morning because we're having a residents' meeting tonight and I'll hear the official version of why we need the increase.”
After I hung up I smiled at myself in the mirror. I told my image that I wasn't trying to get back at Carol, but if she was doing something that wasn't completely legitimate, it should be brought out in the open.
CHAPTER 24
I thought I was good with numbers, but Wesley had over 40 years of practical experience in dealing with columns of figures, and I was immediately awed by his wizardry.
When I showed him Carol's code I told him it had been copied from her notebook, but I didn't provide any details as to how it had come into my possession. Thankfully, he didn't. I briefly went over the thought process I had gone through to determine that the letters must represent numbers.
He agreed with me and said, “In fact, this has a familiar look to it. I was just examining the check register for Silver Acres. The check numbers are four digits; the first column in your code could be check numbers.”
While he sorted through some papers, looking for the check register, he said, “Last night, Carol told the assembled multitudes the reason we need a fee increase is because of a temporary cash flow problem. She gave a reason for it but her explanation was too tortuous and I couldn't follow it. And anything I can't follow I won't buy. She emphasized the temporary nature of the problem and promised there wouldn't be another fee increase next January.”
“So you voted against it?” I said, wondering how I would have voted.
“The vote is going to be taken by mail to ensure that everybody gets a chance to vote. It has to be favored by a majority of all residents. Ah, here we are.” Wesley pulled out a number of pages of computer printout.
“The current check numbers are in the 6,000 range,” he said. He compared it to the code. “The S can't be a six because there are too many different second digits. It's probably a five. Which makes P equal to four. Here's an SS or 55, which confirms it because they haven't reached 6600 yet.”
“If these are check numbers,” I said, they cover a range of 1600 to 1800 checks. They must write a lot of checks here.”