 hile
laboring over the clues for the first Cross-Number
Puzzle, a certain puzzle writer fashioned an inventory of interesting
integers from which to make selections, including primes and powers, factorials
and Fibonacci numbers. Also quite interesting are the Sums of the
First n Integers, but they were not tabulated, for as we learned in Roulette's
Frets, each sum, no matter how large, can be readily calculated as
needed. But wait, there was a problem with the Least
Significant Digits in those sums.
Some ciphers, it seems, are extremely rare, which can be mighty inconvenient when one is creating a puzzle.Rare? No, they were altogether. An exclamation point may be appropriate, inasmuch as a discovery is at hand. Not a big discovery, maybe, but -- hey this is the kind that applies a particular power of perception. And it takes practice. Oh sure, discoveries are conventionally made by looking and listening, thereby seeing and hearing what's there to be seen and heard. The sophisticated solver, though, will recall one of the most famous Sherlock Holmes stories... |
"A dog was kept in the stables, and yet, though someone
had been in and had fetched out a horse, he had not barked enough to arouse
the two lads in the loft. Obviously the midnight visitor was someone whom
the dog knew well."
-- from the short story "Silver Blaze"
by Sir Arthur Conan Doyle |
To catch a thief, the sophisticated detective must listen
for what is
not there to be heard. To make a discovery, the
sophisticated solver must look for what is not there to be seen.
Thus, by observing the absence of certain decimal ciphers as the Least Significant Digits in sums of consecutive integers, the sophisticated solver might well be made to wonder... |
