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Solutions for Act III Scene 3 - Permutation

This is no ordinary crossword - indeed, it may be the first of its kind.

But before we can figure out the function of the 7x7 grid, we should look at some of the clues. Some are easier than others: agreements between business rivals, for example, would be CARTELS; a handheld explosive is a GRENADE; and the Rocky training sequence is an example of a MONTAGE. These words, combined with the size of the grid, are enough to suggest that all the answers have seven letters. This helps identify the others. In the order listed, the answers are:

ACROSS
CARTELS
SCEPTRE
NEAREST
INDICES
MEGATON
ANGERED
SERIALS

DOWN
SCARLET
INCISED
RESPECT
GRENADE
EASTERN
MONTAGE
AIRLESS

By this point, and with the title's assistance, another connection should become clear: each DOWN answer is the anagram of an ACROSS answer. Discovering this connection should also help with getting some of the harder answers, like INCISED and AIRLESS.

The question remains: how can we fit all this information into the grid? An obvious thing to try might be arranging the letters in the grid so that the rows are the ACROSS answers and the columns are the DOWN answers, but clearly this isn't possible. But there's a trickier way to do it! For each anagram pair of answers, we can create a permutation matrix - arranging the seven letters so that each row and each column of the grid contains exactly one letter and such that reading from left to right gives the ACROSS answer and reading from top to bottom gives the DOWN answer. Here's an example using CARTELS and SCARLET:

Because some words have repeated letters, there are multiple possible matrices for some pairs, but there is only one combination of solutions such that when you combine the seven matrices into one, they exactly fill the 7x7 grid. Each anagram pair has one letter circled, and these letters spell one of two words: TEASERS, or TESSERA. The latter is not only more thematic, but is the word you get when ordering the circled letters using the order their sources are presented in the ACROSS clues (which, as some may have noticed, are not quite alphabetical).

The answer is TESSERA.

The answer is: tessera