F1 Source Code: Share and Share Unalike.f1

///////////////////////////////////////////////////////////////////////////////
//
// Title: Share and Share Unalike
// Author: NameHere
// Publication: Dell Logic Puzzles
// Issue: April, 1998
// Page: 35
// Stars: 4
// 
// A gang of thieves in London in the early 1800's had an unusual and complex
// method of dividing their booty. The ten men (Andrew, Colin, Dandy Dan, Ethan, 
// Georgie, Jerry, Little Lester, Morgan, Richard, and Vic) were each ranked 
// and given a number, and then arranged into four tiers as shown below. 
// Everyone had to share what he stole with all those of a higher rank, but 
// not with anyone of equal or lesser rank. For example, 8 had to share with 
// numbers 1 through 6, while 2 only had to share with 1 -- who was leader of
// the gang. (Everyone, of course, also got a share of whatever he had brought
// in himself.) During one week, each member was able to contribute one item 
// to the gang's collection (a pair of boots, clock, bag of gold pieces, pie, 
// bag of shillings, silver teapot, tin of tea, top hat, umbrella, and velvet 
// cloak). 
// Can you find the rank, and booty for each man?
//
//
// Four Ranks: First(1), Second (2,3), Third (4,5,6)
//       and Lowest (7,8,9,10)
// 
//             -1-
//          -2-   -3-
//       -4-   -5-   -6-
//    -7-   -8-   -9-   -10-
// 
// 
//  1. The leader (who wasn't Richard) brought a shiny new black umbrella, which
//     he claimed to have found in the rubbish.
//  2. Little Lester (whose number was odd) was in the same rank as the man who
//     brought a magnificent and only slightly damaged long-case clock.
//  3. Although three other members were entitled to a piece of the rather moldy
//     steak and kidney pie that Georgie stole, they let him have it all to himself.
//  4. Vic's number was exactly twice that of the man who found the top hat.
//  5. Richard and Little Lester both got part of the bag of shillings as their 
//     share, but Ethan didn't.
//  6. There were exactly three members who weren't entitled to the tin of tea, 
//     but the others felt generous and let the whole gang enjoy a cup.
//  7. Seven men wasted no time in divvying up the bag of gold pieces.
//  8. The gentleman's velvet cloak (upon which Andrew had no claim) was 
//     contributed by a man with an even number.
//  9. Georgie isn't member #4.
// 10. Jerry's number was exactly three times Colin's, but one less than that of
//     the man who stole a silver teapot.
// 11. The man who contributed the pair of fine leather boots was entitled to a
//     share of Vic's booty as well, and both were entitled to items contributed 
//     by any of the men in the bottom rank.
// 12. Neither Dandy Dan (who didn't bring the velvet cloak) nor Jerry could claim
//     a share of the gold pieces.
// 
///////////////////////////////////////////////////////////////////////////////
//
// query: 
//          all ShareAndShareUnalikeBreakingNews(member,booty)
//
///////////////////////////////////////////////////////////////////////////////
//
// result:
//
// member = [ {Andrew} 7, {Colin} 3, {Dandy_Dan} 10, {Ethan} 8, {Georgie} 6, 
//            {Jerry 9, {Little_Lester} 5, {Morgan} 1, {Richard} 2, {Vic} 4]
//
// booty =  [ {Boots} Colin, {Clock} Vic, {Gold} Andrew, {Pie} Georgie, 
//            {Shillings} Little_Lester, {Teapot} Dandy_Dan, {Tea} Jerry, 
//            {Hat} Richard, {Umbrella} Morgan, {Velvet_Cloak} Ethan]  
//
///////////////////////////////////////////////////////////////////////////////

Thief = Andrew | Colin | Dandy_Dan | Ethan | Georgie | 
        Jerry | Little_Lester | Morgan | Richard | Vic

Booty = Boots | Clock | Gold | Pie | Shillings | Teapot | Tea | Hat | 
        Umbrella | Velvet_Cloak

Booties = Booty->>Thief
Members = Thief->>[1..10]

pred ShareAndShareUnalike(member:: Members, booty::Booties) iff
//  1. The leader (who wasn't Richard) brought a shiny new black umbrella, which
//     he claimed to have found in the rubbish.
    member(Richard) <> 1 & member(booty(Umbrella)) = 1 &

//  2. Little Lester (whose number was odd) was in the same rank as the man who
//     brought a magnificent and only slightly damaged long-case clock.
    member(Little_Lester) mod 2 = 1 & 
    booty(Clock) <> Little_Lester & 
    SameRank(member,Little_Lester,booty(Clock)) &

//  3. Although three other members were entitled to a piece of the rather moldy
//     steak and kidney pie that Georgie stole, they let him have it all to himself.
    booty(Pie) = Georgie & Rank(member,Georgie,3) & 

//  4. Vic's number was exactly twice that of the man who found the top hat.
    member(Vic) = 2*member(booty(Hat)) &

//  5. Richard and Little Lester both got part of the bag of shillings as their 
//     share, but Ethan didn't.
    GreaterRank(member,Ethan,Richard) & 
    GreaterRank(member,Ethan,Little_Lester) & 
    ((booty(Shillings) = Richard & GreaterRank(member,Richard,Little_Lester)) |
     (booty(Shillings) = Little_Lester & GreaterRank(member,Little_Lester,Richard))) &

//  6. There were exactly three members who weren't entitled to the tin of tea, 
//     but the others felt generous and let the whole gang enjoy a cup.
    Rank(member,booty(Tea),4) & 

//  7. Seven men wasted no time in divvying up the bag of gold pieces.
    Rank(member,booty(Gold),4) & 

//  8. The gentleman's velvet cloak (upon which Andrew had no claim) was 
//     contributed by a man with an even number.
    member(booty(Velvet_Cloak)) mod 2 = 0 & 
    member(booty(Velvet_Cloak)) <> member(Andrew) &
    SameOrGreaterRank(member,Andrew,booty(Velvet_Cloak)) &

//  9. Georgie isn't member #4.
    member(Georgie) <> 4 &

// 10. Jerry's number was exactly three times Colin's, but one less than that of
//     the man who stole a silver teapot.
    member(Jerry) = 3*member(Colin) & 
    member(Jerry) = member(booty(Teapot)) - 1 &

// 11. The man who contributed the pair of fine leather boots was entitled to a
//     share of Vic's booty as well, and both were entitled to items contributed 
//     by any of the men in the bottom rank.
    member(booty(Boots)) < 7 & member(Vic) < 7 &

// 12. Neither Dandy Dan (who didn't bring the velvet cloak) nor Jerry could claim
//     a share of the gold pieces.
    booty(Velvet_Cloak) <> Dandy_Dan & 
    booty(Gold) <> Dandy_Dan & booty(Gold) <> Jerry &
    SameOrGreaterRank(member,Dandy_Dan,booty(Gold)) &
    SameOrGreaterRank(member,Jerry,booty(Gold))

///////////////////////////////////////////////////////////////////////////////
// Four Ranks: First(1), Second (2,3), Third (4,5,6)
//       and Lowest (7,8,9,10)
// 
//             -1-
//          -2-   -3-
//       -4-   -5-   -6-
//    -7-   -8-   -9-   -10-
// 
local pred Rank(member::Members, x::Thief, rank:<I[1..4]) iff
    (rank = 1 & member(x) = 1) | 
    (rank = 2 & member(x) >= 2 & member(x) <= 3) | 
    (rank = 3 & member(x) >= 4 & member(x) <= 6) | 
    (rank = 4 & member(x) >= 7 {& member(x) <= 10})  

local pred SameRank(member::Members, x1::Thief, x2::Thief) iff
    (Rank(member,x1,1) & Rank(member,x2,1)) |
    (Rank(member,x1,2) & Rank(member,x2,2)) |
    (Rank(member,x1,3) & Rank(member,x2,3)) |
    (Rank(member,x1,4) & Rank(member,x2,4)) 

local pred GreaterRank(member::Members, x1::Thief, x2::Thief) iff 
    (Rank(member,x1,2) & Rank(member,x2,1)) |
    (Rank(member,x1,3) & Rank(member,x2,1)) |
    (Rank(member,x1,3) & Rank(member,x2,2)) |
    (Rank(member,x1,4) & Rank(member,x2,1)) |
    (Rank(member,x1,4) & Rank(member,x2,2)) |
    (Rank(member,x1,4) & Rank(member,x2,3)) 

local pred SameOrGreaterRank(member::Members, x1::Thief, x2::Thief) iff 
    SameRank(member,x1,x2) | GreaterRank(member,x1,x2)
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