1207 1370 (solution)

by C. Scott Ananian

You should first realize that there are exactly as many numbers in the first paragraph of numbers as there are words in the first paragraph of words. Googling a handful of words from the paragraph should turn up Lewis Carroll’s Through the Looking Glass. And indeed, the words in this book have been numbered, starting from the beginning. The words in the first paragraph describe the details of the rules used, as follows:

IDENTIFYING THE BOOK:

L(1) = one
L(2) = thing
L(11) = nothing
[not much is needed, Through the Looking Glass has major google juice]

ABBREVIATIONS ARE COUNTED AS ONE WORD:

L(19) = black
L(20) = kitten’s  [not present in the puzzle text]
L(21) = fault

L(54) = it
L(55) = couldn’t  [not present in the puzzle text]
L(56) = have

HYPHENATED COMPOUNDS ARE COUNTED AS ONE WORD:

L(164) = great
L(165) = arm-chair [not present in puzzle]
L(166) = half

L(216) = the
L(217) = hearth-rug [not present in puzzle text]
L(218) = all

CHAPTER TITLES ARE IGNORED, ONLY BODY TEXT IS COUNTED:

L(3241) = natural
L(3242) = way.    [end of chapter 1] [not present in puzzle]
L(3243) = I       [start of chapter 2]

ITALICIZED TEXT IS COUNTED AS A NORMAL WORD:

L(4460) = Rose:
L(4461) = I       [italicized in original text, not present in puzzle]
L(4462) = should

Now that we’re oriented, we can translate the title of the puzzle (“Looking-glass words”) and the remaining paragraphs of numbers, written with only words found in Through the Looking Glass:

“One. What word number is the fourth it? Find that many of of. That last of has an even number with a repeated five. Double that number, twice. What’s one more than that?”

The fourth instance of the word “it” is word 54. The fifty-fourth instance of the word “of” is word 3558 (“with a repeated five”). Doubling this twice yields the number 14232; one more than that is 14233.

“Two. Sum the words of Jabberwocky. (After the first eight, the sum should be one less than the last helmet.) Take from this sum the eighth take, then divide by twenty.”

The Jabberwocky poem starts at word 2861 and runs through word 3026. Summing the first eight words gives 2861+2862+2863+2864+2865+2866+2867+2868 = 22916, and the last of ten occurrences of the word “helmet” in the text is word number 22917. Summing the word numbers of the complete poem gives the number 488621. The eighth instance of the word “take” is word number 12801. Subtracting these gives 475820, which can be divided evenly by 20 to yield the number 23791.

“Three. One less than the sixth square.”

The sixth occurrence of the word “square” is word 5908. One less than this is 5907.

“Four. Start at word one, counting all the letters. After the first white there should be thirty. After the first knight there should be thirty nine hundred eighty-seven. How many after the first thought?”

Counting all the letters in all the words up to and including the first occurrence of the word “thought” (word 1657) yields the number 6653.

“Five. Count how many people. Count how many oysters. Count how many ideas. (Sum is twenty five.) People times people times oysters times ideas is?”

There are 13 occurrences of the word “people”. There are ten occurrences of the word “oysters”. There are two occurrences of the word “ideas”. 13+10+2 = 25. 13*13*10*2 = 3380.

“Six. First pretty is a number which nothing divides but itself and one. First said is another such number. First pretty times first said is?”

The first occurrence of the word “pretty” is word 47, a prime. The first occurrence of the word “said” is word 109, another prime. 47*109 = 5123.

“Seven. Begin before first word and mark each “a”, “e”, “i”, “o”, and the letter that sounds like you. Move past alice seven times. You have marked one three three six letters. Move past alice ninety more times. How many letters have you marked?”

Counting all the vowels (not including “y”) in all the words up to and including the ninety-seventh occurrence of the word “alice” (word 7470) yields 11502 vowels.

Now we’ve got the sequence 14233 23791 5907 6653 3380 5123 11502. The initial paragraph included a few words nearby these word numbers, to orient you if you’ve got a slightly corrupted text:

L(14224) = of
L(23767) = the
L(5936) = and
L(6658) = a
L(3337) = the
L(5137) = a
L(11482) = the

The answer clue phrase is found by converting the answers to the questions (14233 23791 5907 6653 3380 5123 11502) from looking-glass numbers back to words:

L(14233) = TANGLED
L(23791) = TALE
L( 5907) = SEVENTH
L( 6653) = WORD
L( 3380) = BEFORE
L( 5123) = SECOND
L(11502) = OPPORTUNITY

Tangled Tale” is the name of a short book of puzzles by Lewis Carroll. The word “opportunity” appears three times in the book; the second time is in this paragraph:

“Ninety-seven answers have been received. Of these, 15 are beyond the reach of discussion, as they give no working. I can but enumerate their names, and I take this opportunity of saying that this is the last time I shall put on record the names of competitors who give no sort of clue to the process by which their answers were obtained. In guessing a conundrum, or in catching a flea, we do not expect the breathless victor to give us afterwards, in cold blood, a history of the mental or muscular efforts by which he achieved success; but a mathematical calculation is another thing.”

The seventh word before “opportunity” is ENUMERATE, the answer to this puzzle.