CiSRA Puzzle Competition 2009 - Solutions

This is the archive of the 2009 Puzzle Competition. Please visit the current competition site for information about the latest Puzzle Competition.

B.2 Reciprocity

The first step is to notice that each line of this puzzle encodes a sequence of numbers. In some lines, the final clue doesn't translate to a number, but to words such as "repeatedly", "never ending", "endlessly". This is an instruction to repeat a set of digits ad infinitum.

The next step is to realise that each encoding is the exact sequence of digits after the decimal point for reciprocals of whole numbers. The puzzle title may provide a clue here.

The encoded numbers are:

0 (nullity)
52 (cards in a deck)
63 (atomic number of europium)
1578 (the year of the Duel of the Mignons)
9 (Nine Inch Nails is an American rock band)
47 (the 47 Society believes this is the quintessential random number)
36 (number of alphanumeric characters; numerals and letters)
84 (Charlton Heston's age when he died)
21 (points makes blackjack)
repeat (over and over)

0.052631578947368421... is the reciprocal of 19.

0 (out for a duck is to get out without scoring any runs in cricket)
then...
6 (to hit the ball over the fence in cricket is worth 6 runs)
repeat (repeatedly)

0.0666... is the reciprocal of 15.

0 (Goose egg is slang for zero)
7 (wonders of the world)
69 (Summer of '69 is a rock song by Bryan Adams)
23 (Michael Jordan's famous basketball shirt number)
repeat (never ending)

0.076923... is the reciprocal of 13.

2 (Two's company, three's a crowd)

0.2 is the reciprocal of 5.

0 (love is a score of zero in tennis)
625 (The year Chinese empress Wu Zetian was born)

0.0625 is the reciprocal of 16.

1 (single)
repeat (ad infinitum)

0.111... is the reciprocal of 9.

1 (solitary)
42 (Douglas Adams' answer to the ultimate question of life, the universe, and everything)
85 (mark required for a in most Australian universities)
7 (the number of deadly sins)
repeat (endlessly)

0.142857... is the reciprocal of 7.

The sequence of reciprocals revealed is:

19 15 13 5 16 9 7

Replacing each number with the corresponding letter of the alphabet spells out a hidden message:

S O M E P I G

"Some pig" is one of the phrases weaved into Charlotte's Web. It refers to the main character of that story, WILBUR.