Few numerical Listeners are a walk in the park, but Elap’s exceptional Relationship
required ropes, harness, helmet and ice axes to reach its stratospheric summit.
Oh, the foothills were a straightforward ascent: the clues to 2-digit answers along with
the useful 21ac limited values for B, u, s, and y to the first 4 squares, and N soon
followed at 121. I and G proved good candidates for 36 and 24 and the first 2 words: “By
usInG”.
The slope became steeper and progress slowed, but I identified N, K and Y for 121, 144
and 169 respectively and w and O as 196 and 225. By this time it was midnight and I felt
I had reached 1 st camp.
I clambered on and derived several more letters and then disaster struck around
2.45am: I fell into a mathematical crevasse. Somewhere in the northeast corner the only
solution I could find for one of the squares ended in 7. Impossible! The only solution was
to retire for the night and approach 2 nd camp with fresh(er) eyes.
I reworked my solution and confirmed By usInG, O and K. Seeking to identify where I
had fallen, I turned my attention to confirming N, w and Y. I found K and spotted that L-a
or its negative appeared 3 times. And – oh joy – both w and Y needed to be 169 or 196
between them. I I had reached 2 nd camp but could not see a logical path to the summit;
examination of every clue yielded no more letters!
I turned to the message. I had By usInG ..NKY wo… and setting aside my desire to
derive the solution logically I made the assumption that the message would read
By usInG WoNKY woRDS
This enabled me to climb steadily and surely towards a filled grid less the 2 unclued
entries. And to face an overhang: what did “By usInG WoNKY woRDS, PiTCH a LAter
clue” mean?
Inspiration was required – and eventually arrived. The last 5 words contain 20 letters,
and wonky looks like an anagram indicator. An online anagram solver gave me
CALCULATE THIRD POWERS – what? These sets of 4 entries not only sum to a
square but divide into A 3 + B 3 = C 3 + D 3 ????
Elap, you have surpassed yourself and others in the field with Relationship. It is a rare
and beautiful numerical which not only poses a consistently challenging solve but
provides an endgame that is both mathematically and cruciverbally satisfying.