# a difference of 29°

The eight words pictured here, along with their positions, can be divided into two groups of four words apiece. Identify the two groups and why each word-position combination belongs to its group.

I apologize for the sloppiness of the words: they were handwritten by mouse so they'd be in the right positions. They are, top to bottom, SKEPTICAL, DAPPLED, COME-ON, SOLO, SACRAMENT, CACCIATORE, IMPRESSION, and WAITING.

Overlaying this picture and a particular other picture will help. What sort of picture do you think that might be, based on the layouts of the words?

Overlaying this picture and a particular other picture will help. What sort of picture do you think that might be, considering that the words are written either ~horizontally, ~vertically, or crowded into a small square?

• Is the angle you mention in the title the angle between the centers of words $i$ and $i+1$ as per the order provided in the picture? Or is it the related to the angle in the font representation of the words (for examlple, 'A' has an angle '^' at the top) Jun 28, 2020 at 17:02
• @JohnBrookfields, I don't think we've reached the point yet where I need to supply a hint. When I do, I'll consider making it an explanation of the title, per your request. Jun 28, 2020 at 18:03
• @JohnBrookfields, I considered it, but decided to go with a different hint for now. Jun 29, 2020 at 8:35
• Onfrq ba ubj gur jbeqf ner jevggra (fbzr ner pbafgevpgrq fhpu nf FBYB va n irel fznyy fcnpr va 2 yvarf jura 1 vf rabhtu naq FXRCGVPNY ntnva univat 2 yvarf va yvrh bs 1.). Guvf ercerfragf gur ertvba bs inyvqvgl bs gung gur jbeq ercerfragf vf yvzvgrq va "fcnpr". Fb, qbrf guvf zrna gur uvag cbvagf gb n znc? @msh210 Jun 29, 2020 at 9:00
• @JohnBrookfields My guess is we're looking at either rot13(n trbtencuvpny znc be n pbafgryyngvba) since both of these involve degrees (as per the title)...
– Stiv
Jun 29, 2020 at 9:12

One group contains...

SKEPTICAL, DAPPLED, COME-ON, SACRAMENT

...because...

each of these words (and its corresponding Manhattan location based on the image) appears in the lyrics of songs by Simon & Garfunkel.

And the other contains...

SOLO, CACCIATORE, IMPRESSION, WAITING

...because...

each of these words (and its corresponding Manhattan location based on the image) appears in the lyrics of songs by Billy Joel.

Explanation of each word:

SKEPTICAL

"Orangutans are skeptical"
Simon & Garfunkel - At the [Central Park] Zoo

DAPPLED

"I'm dappled and drowsy and ready to sleep"
Simon & Garfunkel - The 59th Street Bridge Song (Feelin' Groovy)

COME-ON

"Just a come-on from the whores on Seventh Avenue"
Simon & Garfunkel - The Boxer

SOLO

"Crazy Latin dancing solo down in Herald Square"
Billy Joel - Rosalinda's Eyes

SACRAMENT

"Holy, holy is his sacrament"
Simon & Garfunkel - Bleecker Street

CACCIATORE

"He works at Mister Cacciatore's down on Sullivan Street"
Billy Joel - Movin' Out (Anthony's Song)

IMPRESSION

"I guess I made an impression on somebody"
Billy Joel - Big Man on Mulberry Street

WAITING

"The boats were waiting at the Battery"
Billy Joel - Miami 2017 (Seen the Lights Go Out on Broadway)

And a quick mockup of how the image spatially relates to the puzzle, as suggested by the hints:

• This is a fantastic first answer - well done :) Any chance you could point out these locations on a map to round it all off perfectly, since the question does talk of overlaying the image? Thanks, and a thoroughly deserved +1
– Stiv
Jul 9, 2020 at 21:30
• AH great work! Really impressed with the mental leap you made. Jul 9, 2020 at 22:22

I am 100% convinced that the thing to overlay is a map of Manhattan.

Because:

Manhattan, in its maps, is rotated 29 degrees so it appears as if it is directly north to south.

And also because:

Things like parks and blocks are square while roads are written out longways.

That being said,

I'm really struggling to find the appropriate overlay in which the items match up properly (I think "DAPPLED" is probably one of the bridges?)

Other thoughts so that someone else can maybe finish this up:

"Cacciatore" could be referring to Little Italy, or to a street beginning with C (SOHO seems promising because there's Centre, Church, etc. and Spring St.).

Different maps of Manhattan have different proportions - I tried on an actual geographically correct map as well as the NYC MTA map and couldn't find a match with either.

I think "Waiting" somehow aligns with the road down by Battery Park at the very bottom of Manhattan.

• Excellent find! Your main point is correct. And some of your other points are correct, or nearly so: in particular, what you said about DAPPLED is correct. As an additional hint, rot13(jung qbrf gung jbeq unir gb qb jvgu bar bs gur oevqtrf)? Jul 1, 2020 at 22:10
• My best guess there is Gur oevqtr gung gur frira genva tbrf npebff orpnhfr QNCCYRQ unf frira yrggref. Gubhtug nobhg Oebbxyla Oevqtr orpnhfr oebbxf ner... qnccyrq? Ohg V'z abg fher. Jul 1, 2020 at 22:23