Thirteen Diamonds

coded message of this length. It didn't look like the English alphabet. I couldn't assume that the character with the count of 20 was E because there were also counts of 18, 16 and three 15's. And I couldn't find enough repetitions of the same three characters to pick out common words like “the” and “and.”
    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