Last week’s puzzle wasn’t quite thematic, but it was built around a few entries that interacted closely with each other. Without giving too much away for those who haven’t solved it yet, suffice it to say that there are certain entries in the puzzle that are defined (and/or clued) only in terms of other entries—and vice versa.

This sort of mutual cross-reference is a trick we like to invoke from time to time. The most common motivation is to use it as a vehicle for showing off a pair of long anagrams. For example, Puzzle #3264 included this matched pair of clues:    1 (OPERATING COST)  Expense for a business ruined 27 (9,4)    27 (PROGNOSTICATE)  Predict 1A inaccurately (13)

Or in Puzzle #3300:    13 (ISAAC STERN)  Violinist playing 21 (5,5)    21 (ASCERTAINS)  Discovers unlucky 13 (10)

Some skeptics might complain about these clues, because in each case neither one can be solved without reference to the other. If you’re a firm believer that each clue in a cryptic crossword should be its own independent solving challenge, for example, then you’d be apt to see these as not quite fair.

But we believe that a clue should be considered in the context in which it appears. And if there’s helpful information from somewhere else in the grid that can lead a solver to the solution, there’s no reason not to use it. For many solvers, this adds to their enjoyment: The penny drops for both clues in quick succession, usually after letters are provided by crossing entries. And for expert solvers, it is interesting to see how early in the game they can crack the pair. During a test-solving session, we were stunned to see crossword champion Tyler Hinman get OPERATING COST / PROGNOSTICATE before entering a single letter into the diagram.

In fact, such mutually reinforcing clues are just an extreme case of a more general technique that many constructors use freely, namely the one-way cross-reference. In those cases, one clue is solvable on its own, and a second then relies on that answer. The two most common uses are as anagram fodder, as in this pair from Puzzle #3343:    19 (BEEP)  Buzzer on front of porch makes sound heard in the street (4)    2 (REPUTABLE)  Ultra-19 eccentric is well-regarded (9)

or as part of the definition, as in this pair from Puzzle #3320:    24 (SATAN)  Old Nick took a chair on the outskirts of Austin (5)    23 (EVIL)  Upset to be like 24 (4)

These cross-references aren’t as snazzy as the circular constructions, which have a little whiff of M.C. Escher about them. But both are useful resources in a constructor’s bag of tricks and, we hope, an entertaining change of routine for the solver.

This week’s clueing challenge: MUTUAL. To comment (and see other readers’ comments), please click on this post’s title and scroll to the bottom of the resulting screen. And now, four links: • The current puzzle • Our puzzle-solving guidelines | PDF • Our e-books (solve past puzzles on your iOS device—many hints provided by the software!) • A Nation puzzle solver’s blog where every one of our clues is explained in detail. This is also where you can post quibbles, questions, kudos or complaints about the current puzzle, as well as ask for hints.