CiSRA Puzzle Competition 2013 - Solutions

5B. Circular Definitions

The trick to this puzzle is that each of the definitions given is a definition of two different words, and that each word has two definitions. Each word fits into the circle in between two of the definitions, and in each of those places is a set of numbers. The definitions and matching words (along with the numbers) are listed below.

Set burning.
    FIRE (7,2/4)
To discharge or release.
    SECRETE (15,1/7)
Kept secret.
    INSCRUTABLE (12,10/11)
Incapable of being understood.
    IMPENETRABLE (3,11/12)
Incapable of being taken by force; strong enough to withstand attack.
    IMPREGNABLE (14,2/11)
Capable of becoming pregnant.
    FERTILE (11,1/7)
Abounding in natural resources.
    RICH (6,1/4)
Having an abundance of wealth, property, or other material goods.
    AFFLUENT (2,1/8)
A stream that flows to a larger stream or other body of water.
    TRIBUTARY (16,9/9)
Subject; dependent.
    SUBORDINATE (5,3/11)
Lower in station, rank, degree, or grade.
    INFERIOR (13,1/8)
Having low quality.
    POOR (1,1/4)
Having little or no money.
    BROKE (4,5/5)
To have fragmented something into multiple parts, no longer functional.
    SMASHED (9,5/7)
To have had an excess of liquor.
    SPIRITED (10,6/8)
Stimulated, revved up, excited.
    IGNITED (8,2/7)
(Set burning)

The remaining step is to use the numbers given in the form 1st,2nd/3rd. The third number is the number of letters in the word (this can be deduced and used to help solve the clues). The first number takes the values 1 to 16, suggesting an ordering. The middle number may be read as forming a/b, where b is the total number of letters, suggesting that it is referring to the ath of the b letters, i.e. use it as an index into the words. Indexing with the middle number and sorting by the first numbers gives the message:

PALEBRIGHTFLIMSY

Pale, bright, and flimsy are again multiple meanings of a single word, in particular the word LIGHT, which is the solution.