1. Chantele does not do Lazy Lad
2. Beriberi does not do Jagged Edge
3. Rhapsody does not do Double Dip
4. Marianne does not do Double Dip
5. Slowride does not do Yankee Swap
6. Pink Lady, Black Cat do not do Double Dip, Pop the Weasel, Quick Trip, Walk the Cat => they do either Jagged Edge, Lazy Lad, Rope Burn, or Yankee Swap

1. \$ Pop the Weasel = \$ Double Dip = \$ Quick Trip = \$ Walk the Cat - \$50
2. \$ Walk the Cat < \$ Black Cat = \$ Pink Lady / 2
3. \$ Rope Burn > \$ Yankee Swap
4. \$ Pink Lady +- \$50 = \$ Beriberi > \$ Jagged Edge
5. \$ Chantele < \$ Lazy Lad

1. \$ Pop = \$ Double = \$ Quick < \$ Walk < \$ Black Cat < \$ Pink Lady
2. since \$ Pink Lady >= \$125, we know that \$ Pink Lady - \$50 > \$ Black Cat. Therefore, either \$ Black Cat < \$ Beriberi < \$ Pink Lady or \$ Black Cat < \$ Pink Lady < \$ Beriberi
3. Walk is not the second least expensive service lest \$ Pop = \$ Walk - \$ 50 = \$ 125 - \$ 50 = \$75.
4. Therefore, we need either \$ X < \$ Pop < \$ Walk or \$ Pop < \$ X < \$ Walk.
5. There are 7 distinct acts already in the hierarchy so there can be no other acts < \$ Walk.
6. X cannot be Rope Burn because \$ Yankee < \$ Rope.
7. X cannot be Jagged Edge, since \$ Jagged Edge = 2 * \$ Y, \$ Y < \$ Hyacinth.
8. X can be Lazy or Yankee. Since \$ Z < \$ Chantal < \$ Lazy it cannot be Lazy. And \$ Yankee is not the cheapest, it must be that \$ Pop < \$ Yankee < Walk.
9. Thus, we know that \$ Yankee = \$125, and because things are in \$25 increments, necessarily \$ Pop = \$ Double = \$ Quick = \$100, \$ Walk = \$150

## Correct

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 slowride.
1. Then by the average, marianne/rhapsody must cost 200. but then rhapsody is not greater than chantele and marianne is not more than black cat.
8. so it cannot be slowride. third must be chantele.
9. fourth 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.
 Rhapsody/Marianne Quick Tip 100 Hyacinth Yankee Swap 125 Chantele Walk the Cat 150 Slowride Jagged Edge 200 Marianne/Rhapsody ? 300 Beriberi ? 400