Whos Your Daddy

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Puzzle Boat

[1]

Logic

1. Someone costs less than them: Black Cat, Pink Lady, Beriberi, Chantele, Hyacinth. This leaves Rhapsody, Marianne, Slowride. Slowride cannot be it because she is the average between rhapsody and marianne. Either rhapsody or marianne must be the least.
2. The following acts cannot be the cheapest (rope burn, double dip, pop the weasel, lazy lad, walk the cat, yankee swap, jagged edge). This leaves just quick trip.
3. assume that the second is unique (at $125). Then quick tip = $100, second = $125, walk = $150.
4. the following cannot be the second: rope, walk, quick, lazy, pop, jagged. This leaves yankee and double. but if double dip is second = 125, then pop = double+quick = 225 which is disallowed. thus yankee is second.
5. the person who does yankee swap cannot be the following: chantele, beriberi, rhapsody, marianne, slowride, pink lady, black cat. That leaves just hyacinth.
6. since the only woman below hyacinth costs 100, jagged edge must cost 200 and beriberi 400.
7. the following people cannot be third: rhapsody, marianne, pink lady, beriberi, hyacinth, black cat. That leaves chantele and slowride. Time for speculation. Assume chantele.
   1. jagged cannot be the following: rhapsody/marianne, hyacinth, chantele, beriberi, pink lady. That leaves black cat, slowride, marianne/rhapsody. It cannot be black cat because then pink lady would cost $400. It cannot be marianne/rhapsody for then their average would be 150 which cannot be slowride. thus, it must be slowride. This implies that marianne/rhapsody costs 300.
   2. The cost for pink lady is either 450 or 350. If it is 450, then black cat is 225 which is disallowed. Thus pink lady is 350 and black cat is 175.
   3. Now it is impossible to have 100+175 or 350 = 350 or 400 (rule 4). Thus we have speculated incorrectly.
8. Third is slowride. By averages, marianne/rhapsody = 200. Thus marianne/rhapsody are jagged.
9. By rule 11, we must have that black cat is at 175, and that first is rhapsody. The logic for pink lady holds as before.
10. We now that someone has a service for $300 so that must be chantele.
11. Possible ones for double dip are black cat, chantele, pink lady, beriberi. When added to quick tip, this gives 275,400,450,500. Since 400 is the only valid one, we know that chantele is double dip, and beriberi is pop.
12. By rule 1, Pink Lady must be Lazy Lad.

Rhapsody	Quick Trip	100
Hyacinth	Yankee Swap	125
Slowride	Walk the Cat	150
Black Cat	Rope Burn	175
Marianne	Jagged Edge	200
Chantele	Double Dip	300
Pink Lady	Lazy Lad	350
Beriberi	Pope Goes the Weasel	400

Decoding

STRING: RYOCAEDI

KEY: CHANTELE

Answer: PROPHASE