Sam wanted to do a romantic show of love for her girlfriend Amy for Valentine’s Day. Sam printed out 14 giant heart-shaped lawn signs, each printed double-sided with a red side and a purple side, and each with a character (letter, symbol, or space) printed on each side. When the signs were set up so that the red side faced Amy’s window, the signs spelled: “I LOVE YOU AMY.” At midnight, each of the signs would be flipped around so that the purple sides faced Amy’s window, spelling the name of a New York destination where Sam would be waiting with flowers.
Unfortunately, Sam’s friends were a bunch of goofballs, and the signs weren’t set up quite properly. Fortunately, the signs were at least printed correctly and set up in the correct respective locations. But some of the signs were set up with the purple side facing Amy’s window, whereas other ones were set up with the red side facing her. Can you figure out how the signs were oriented, and figure out where Sam is waiting in New York?
- At least five red signs and at most nine red signs are visible from Amy’s window.
- If #1 has the same character visible as #9, then #2 has the same character visible as #4.
- If #6 and #8 show the same character, then sign #13 is red.
- If sign #1 has an R, S, or T visible, then there are exactly seven distinct characters visible.
- If sign #11 shows a letter in the second half of the alphabet, then sign #10 shows an R.
- If sign #2 and sign #5 are different colors, then sign #10 shows a D.
- If sign #2 and sign #5 are the same color, then sign #11 shows a C.
- If sign #3 and #9 have different characters visible, then one of those letters is an O.
- If sign #3 and sign #4 are the same color, then sign #13 shows a consonant.
- If sign #4 is purple, then sign #5 is red.
- If sign #4 is red, then sign #1 shows a letter in the second half of the alphabet.
- If sign #7 shows a G, H, I, J, or K, then sign #8 shows N or O.
- If sign #9 and sign #10 both show vowels, then #11 shows either a B or an X.
- Both #3 and #11 show letters. If the letter on #3 comes after the one on #11 alphabetically, then #2 shows a space character.
- If there is an odd number of purple signs visible, then sign #9 has S visible.
- Sign #1 has an A, I, S, or U visible.
- Sign #12 has an A visible.
- Six of the signs have vowels visible.
- The number of red signs is equal to the number of Es visible.
- The number of Rs visible is either zero or two.
- There are at least six and at most twelve distinct characters visible.
- If sign #10 shows a vowel, then sign #13 shows a K or L.
- If sign #12 shows B, E, or T, then signs #6 and #7 show adjacent letters of the alphabet.
- If sign #12 shows one of the first three letters of the alphabet, then signs #1 and #6 show adjacent letters of the alphabet.
- If sign #13 shows an I, J, or K, then sign #2 shows an ampersand or the letter U.
- If sign #13 shows an L or M, then sign #8 shows an N or O.
- If sign #2 shows a letter of the alphabet, then sign #5 shows a hyphen.
- If sign #2 shows a vowel, then sign #3 shows a vowel as well.
- If sign #5 does not show C, then sign #2 shows a letter in the first half of the alphabet.
- If sign #5 shows a non-letter symbol, then sign #12 shows an H, T, or Y.
- If sign #6 shows H, O, P, or E, then sign #12 does not show C.
- If sign #7 is red, then sign #12 shows one of the first five letters of the alphabet.
- No even-numbered sign shows the letter J, Q, or X.
- Of the five letters D, O, U, B, and T, exactly two of them appear on the visible side of a sign (possibly multiple times each).
- The letters E and K are never adjacent.
For purposes of this puzzle, Y is not a vowel.
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