The Beekeeper's Apprentice - Laurie R. King [135]
Holmes and I had discussed the possibility that the series was based on a number/letter substitution code, in which, for example, 1 might be read as A, 2 as B, and 3-1-2 translates as CAB. Extreme complexity—basing the substitution on a key text, primarily—is com-monly used to make the translation from number to letter difficult: A long message in such a code can be broken by a bit of fiddling, but for short phrases, one must discover the key. If the key is something ex-ternal, such as the words on a page of a book, decoding a brief message such as the one we were faced with may prove virtually impossible.
In this case the numerals used were not our Arabic ones, but Ro-man ones, and as they had not been spaced or had their divisions marked, it was sheer guesswork to know whether there were twenty-five separate numbers, or only seven, or some total in between. That is where Holmes and I had left off, as we could make no sense in the number/letter result we had extracted.
I had to make a few basic assumptions in looking at the problem. First of all, I had to assume that she had left it there for us to see and, eventually, understand, that it was not just a means of maddening us with tantalising clues that led nowhere. Second, I had to believe that the key to it lay somewhere in front of me, waiting to be seen. Third, I assumed that once the key was found, it would unlock the puzzle fairly quickly. If it did not, I would undoubtedly conclude that this was not the correct key and lay it down again. To give an example, it would call for a boneheaded sort of persistence to unravel the Roman numeral series XVIIIXIIIIXXV through all its possible Arabic equiva-lents into the numbers 18-13-1-25, and then into RMAY, and then fi-nally to unscramble it to MARY, unless the person already knew what she was looking at. No, the key would not give too much difficulty once it was inserted into the lock. Of that I was certain.
If I was right, the key had been found by the still, small daughter of a voice and laid into my dream for me to find. Henry VIII meant noth-ing to me, but VIII, or base eight, meant a great deal. If human beings had been born with three fingers instead of four opposing their thumbs, we would count by units of eight instead of tens. A one plus a zero would mean eight, 11 would be how we wrote nine, and 20 would be the same as a base ten sixteen. I wrote it out on a piece of paper, the first twenty-six numbers in base eight with the alphabet underneath:
1 2 3 4 5 6 7 10 11 12 13 14 15
ABCDEFGH I J K LM
16 17 20 21 22 23 24 25 26 27 30 31 32
NOPQRS TUVWXY Z
I was left with the problem of dividing up the twenty-five Roman numerals into numbers whose letter equivalent said something. Al-though I knew them by heart now, backwards and forwards, I wrote them out too as a visual aid:
XVXVIIXXIIXIIXXIIXXIVXXXI
Twenty-five numerals, ones, fives, and tens. Taken at its most straightforward, these yielded a series of Hs, Es, and As, which would be meaningless. My job was to divide that string up so that the letters made sense.
I began with the first ten numerals, XVXVIIXXII. That last I might be attached to the following X to make nine, but I should keep that possibility in mind. XVXVI, or 10-5-10-5-1, yielded H-E-H-E-A, which, unless she wanted to show her derisive laughter, made no sense. Taking the first XV as 15 gave me MHEA. X-V-XVII = 10, 5, 17 gave HEO, which was better than the other. Higher numbers gave the great-est variation of the alphabet. I tried using the highest possible numbers I could get from the twenty-five