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# Solution to The Unambiguous Osculation

by Kevin Wald

Each four-way kissing session described:

1. Refers to a specific romantic comedy film (with the three non-first-person characters being participants in a love triangle).

These films start with the letters A though N, thus providing an ordering.

2. Corresponds to an arrangement of four mutually osculating (tangent) circles (as hinted at by the "other romantic shapes" in the flavortext, and "circles" in the verse).

Descartes' Theorem gives a simple relation among the curvatures (reciprocals of radii, counted as negative for an enclosing circle) of sets of such circles:

(W + X + Y + Z)2 = 2(W2 + X2 + Y2 + Z2)

which enables you to get the two possibilities for one curvature from the other three by:

W = X + Y + Z ± 2 * sqrt(XY + YZ + XZ)

We treat the "bendiness scores" as curvatures, as indicated in the verse (note that the characters who "embrace" the others have only the absolute value of the bendiness specified, since the value used in the formula must be negative) and get the score for the first-person speaker (taking the "high" or "low" bendiness as indicated), giving us:

DescriptionFilmXYZW1W2Wd. in verse1st SoundWd. in Soddy Poem1st Sound
"Pinky" (bendiness score 0.1) and "Pinkie" (bendiness score 2.5) were kissing after their big court case, and Kip (bendiness score 8.4) came along and kissed both of them — no bones about it, I (at low bendiness) just had to kiss all three! (1949)Adam's Rib0.12.58.41.620.4no/n/kiss/k/
As she (bendiness score 1.6) mentioned in her journal, when Daniel (bendiness score 0.4) and Mark (bendiness score 8.5) and I (at low bendiness) all kissed her, we would also kiss each other! (2001)Bridget Jones's Diary1.60.48.52.118.9our/aʊ/involves/ɪ/
That New England mistletoe was powerful enough to get Elizabeth (bendiness score 5.9), John (bendiness score 0.6), Jefferson (bendiness score 0.2), and me (at low bendiness) all kissing each other! (1945)Christmas in Connecticut5.90.60.22.311.1yes/j/trigonometry/t/
Having deduced that Bunny (bendiness score 2.0) and Richard (bendiness score 0.9) and I (at high bendiness) were all kissing, Emmy (|bendiness score| = 0.4) made a calculated move, and embraced all of us and kissed us! (1957)Desk Set2.00.9-0.40.94.1oops/u/each/i/
Being in a three-dimensional world made it much easier for Giselle (bendiness score 4.8) and Edward (bendiness score 0.4) and Robert (bendiness score 0.4) and me (at high bendiness) all to kiss each other! (2007)Enchanted4.80.40.41.69.6Zoom/z/is/ɪ/
When Peter (|bendiness score| = 0.3) finally remembered that that actress (bendiness score 2.0) and Rachel (bendiness score 9.3) and I (at low bendiness) were kissing on the beach, and embraced all of us, we all kissed him! (2008) Forgetting Sarah Marshall-0.32.09.33.218.8sets/s/not/n/
Harold (bendiness score 0.2) overcame his timidity with Mary (bendiness score 1.8), and with Ronald (bendiness score 2.7) and me (at high bendiness), and you wouldn't have heard a word from any of us during that big mutual kissfest! (1924)Girl Shy0.21.82.7-0.19.5on/ɑ/then/ð/
Extra! Extra! Walter (bendiness score 6.9) kissed Hildy (bendiness score 1.6), who kissed Bruce (bendiness score 0.4), who kissed Walter, who kissed me (at low bendiness) while I kissed Hildy and Bruce, in a pre-weekend free-for-all! (1940) His Girl Friday6.91.60.41.316.5don't/d/of/ə/
As Howard (bendiness score 8.4) kissed Peter (bendiness score 0.6) while I (at low bendiness) kissed them both, Emily (|bendiness score| = 0.2) embraced us all, kissing Howard and Peter stylishly but me less so! (1997)In & Out8.40.6-0.25.212.4each/i/bring/b/
When Leslie (bendiness score 0.2) and Morgan (bendiness score 0.3) and I (at high bendiness) kissed Scott (bendiness score 3.8), we also kissed each other to give him time to recover! (2010)Just Wright0.20.33.81.57.1zir/z/if/ɪ/
She (bendiness score 2.2) and Josh (bendiness score 1.5) and Helen (bendiness score 0.3) and I (at high bendiness) all . . . well, you know! (2001) Kissing Jessica Stein2.21.50.3-0.28.2pick/p/gets/g/
I (at high bendiness) kissed David (bendiness score 1.4) and Natalie (bendiness score 2.6) as they kissed each other, and the President of the United States (|bendiness score| = 0.1) embraced all of us and kissed us — with affection in fact! (2003)Love Actually1.42.6-0.10.37.5ode/oʊ/beyond/b/
There was nothing plastic about the way Emmy (|bendiness score| = 0.3) embraced Jonathan (bendiness score 7.7) and Roxie (bendiness score 0.8) and me (at low bendiness), and kissed us while we kissed each other! (1987)Mannequin-0.37.70.84.412amiss/ə/other/ʌ/
It was very comradely how she (bendiness score 0.3) kissed Leon (bendiness score 9.9), and Swana (bendiness score 1.2) kissed both of them, and all three kissed me (at low bendiness)! (1939) Ninotchka0.39.91.23.619.2means/m/circles/s/

The bendiness values we get are (as indicated by the verse) used to select words from the verse. Specifically, we take the numbers before and after the decimal point as the line and word number. As indicated by the verse, we take the initial sounds of these words, to get (as seen in the chart above) "now use soddy's poem." In 1936 Frederick Soddy rediscovered Descartes' Theorem, and published the result in the form of a poem, "The Kiss Precise" (to which the puzzle's title alludes), whose first stanza is:

For pairs of lips to kiss maybe
Involves no trigonometry.
‘Tis not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.

Repeating the process with this poem gives "kitty in the big bus/buss." The answer is the actress who played Kitty in the movie The Big Bus, STOCKARD CHANNING.