A belated GAG27 cache ...
The cache is NOT at the posted coordinates. Do NOT go there to search for it. Your search would be unproductive, extremely dangerous, and illegal (unless it were quite fleetingly inside an approved vehicle moving in an appropriate direction at a suitable speed). Your mother probably warned you never to play in traffic, and we strongly concur with that advice. Instead, to find this cache, you will need to follow the instructions below (just after our apology).
We admit it. Mistakes were made. We (MAPSIT & waxwing454) made them – dicey math, ambiguous questions with different reference sources giving different answers, awkwardly implemented changes to the cache page to remedy things – you name it. Geocachers were inconvenienced. It was a sorry cache, and we’re sorry, truly sorry. So, lest it be a matter of just words, some sort of recompense is in order. And since we’re members of a geocaching community, we’ve been politely, but firmly, told that it should take the form of a new (if rather late) GAG27 cache, being of the same general form of our earlier, infamous, less than perfect, sorry excuse for a GAG27 cache. And in the immortal words of Kenny Loggins, Michael Jackson, and Scotty McCreery (but not either simultaneously or collaboratively), “This Is It.”
Once again, as stipulated, it’s a puzzle cache, but this time we give you all the information you should require to get the relevant answers to the several questions, all of them involving well-known "sorry" songs; indeed, we'd have given you the specific URLs we used for the song lyrics you'll need, but there was a concern that the references we used might contain commercial content, so you'll just have to figure out your own searches, though boomers likely won't even need to look things up. Lest there be doubt about the nature of the desired responses, we’ve not only made them all one-word answers, but also given you the number of letters in the correct responses (most of them pretty small), along with the relevant parts of speech, and some very strong hints via the song titles. We think we’ve made sure that the math is correct, and because some geocachers have complained about having to understand sixth grade math such as prime numbers, Fibonacci numbers, exponentiation, or modulo/remainder functions, we’ve kept everything to digital roots and four function arithmetic, though we did throw in a few parentheses to make the math even clearer. And for those geocachers just wanting to bump up their smiley count with this one, we’ve placed the cache where it should be winter friendly and readily accessible. Oh yeah, and there's a geochecker too. And if you're STILL having trouble with the puzzle, just message one of us and we'll give you as many hints as you want. We think that the only real danger involved in this cache is earworms, but because there’s no icon for them, we’ve not included those in the attributes, or in setting the difficulty level for the cache - you've been warned; don't blame us should you choose to proceed with the puzzle.. The terrain rating refers to the actual cache location, and emphatically NOT the posted coordinates (for which, again, DON’T go there, PLEASE). Since the theme for GAG27 is games, please consider this puzzle an instance of the ubiquitous "complete the lyrics" game, except that you don't, as in several of the televised implementations, get a pie in the face if you aren't immediately successful.
Stage 1: Derive six single digit values from six “sorry-themed” songs – U, V, W, X, Y, and Z. Identify the songs, and answer each of the questions with a single word from the associated song's lyrics, and for each, to get the desired digit, take the digital root of that word. To make your life even easier, we've made sure that the relevant word is close to the word "sorry" in the lyrics, and we've even included a character string consisting of the first letters in each word of the relevant song title -- e.g., if the relevant song were "Old Macdonald Had a Farm," the string would be OMHAF.
U: What kind of word does Elton John think that sorry is? ____ (SSTBTHW - 7 letter adjective, superlative form) DR = ____.
V: What does a sorry Brenda Lee ask you to accept? her ___ (IS - 7 letter noun) DR = ____.
W: What verbal technique does Chicago use to convey its sorrow? ____ (HTSIS - 3 letter verb) DR = ____.
X: What is the time frame for Connie Francis’s query about sorrow? _____ (WSN - 3 letter adverb) DR = ____.
Y: How sorry does Paul McCartney indicate to Uncle Albert that they are? ____ (UA/AH - 2 letter adverb) DR = ____.
Z: What action is John Lennon sorry that he made someone do? (hint: second person singular, 2nd hint: the Imagine album) ____ (JG - 3 letter verb) DR = ____.
Stage 2: Derive the coordinates of the hide.
The cache is at N 45 19.ABC, W075 53.DEF. Use some simple four-function math (OK, sometimes with parentheses) to derive the single-digit values for A through F from the values of U through Z that you derived as digital roots in Stage 1, where
A = U – V - Z - V
B = W – X
C = W - X + Y – Z - U
D = X - U*(V + Z) + X/Y
E = Y – (V + Z)
F = ((U*V)+3) +W/Z -(X+Y) – V