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Merge pull request csplib#129 from ozgurakgun/cross-figures
Crossfigures
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‎Problems/prob021/models/Crossfigures.essence

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language Essence 1.3
22

3-
given nbDom : int(1..)
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letting dom be domain int(1..nbDom)
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given bound : int(1..100)
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letting Postion be domain (int(1..bound),int(1..bound))
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given numDigits : int
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given dimension : int
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8-
given numClues : int(1..bound**2)
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letting Clue be domain int(1..numClues)
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letting Arg be domain int(1..numClues)
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letting digit be domain int(0..9)
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letting number be domain int(0..10**numDigits)
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letting Type be new type enum {Add, Modulo}
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$ locations
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given l : function (total,injective) Clue --> (Type, Arg, Arg, Postion )
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find grid : matrix indexed by [int(1..dimension), int(1..dimension)] of int(0..9)
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branching on [grid]
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1612

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find grid : matrix indexed by [int(1..bound),int(1..bound)] of dom
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$ the black blocks
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given blackCells : set of (int, int)
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such that
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forAll (row, col) in blackCells . grid[row,col] = 0
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given acrossClueCoords : set of ( int $ seq
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, int $ the row
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, int $ the starting column
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, int $ the ending column
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)
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letting acrossIndex be domain int([i[1] | i <- acrossClueCoords])
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find across : matrix indexed by [acrossIndex] of number
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find acrossDigits : matrix indexed by [acrossIndex] of sequence (maxSize numDigits) of digit
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such that
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forAll (seq, row, colStart, colEnd) in acrossClueCoords .
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acrossDigits[seq] = [ grid[row,col] | col : int(colStart..colEnd) ]
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given downClueCoords : set of ( int $ seq
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, int $ the col
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, int $ the starting row
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, int $ the ending row
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)
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letting downIndex be domain int([i[1] | i <- downClueCoords])
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find down : matrix indexed by [downIndex ] of number
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find downDigits : matrix indexed by [downIndex ] of sequence (maxSize numDigits) of digit
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such that
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forAll (seq, col, rowStart, rowEnd) in downClueCoords .
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downDigits[seq] = [ grid[row,col] | row : int(rowStart..rowEnd) ]
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$ connecting digits to numbers
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such that
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forAll n : acrossIndex .
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across[n] = sum (i,d) in acrossDigits[n] . (10**max([0,|acrossDigits[n]|-i])) * d,
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forAll n : downIndex .
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down[n] = sum (i,d) in downDigits[n] . (10**max([0,|downDigits[n]|-i])) * d
1850

1951

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$ first digits are >1
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$ this is probably implied, but having it just in case.
2054
such that
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forAll n : acrossIndex . acrossDigits[n](1) > 0,
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forAll n : downIndex . downDigits[n](1) > 0
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letting AD be new type enum {A, D}
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letting CLUE be domain
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variant
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{ is_constant : int
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, is_square : bool
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, is_prime : bool
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, plus_constant : (int, AD, int)
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, minus_constant : (int, AD, int)
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, times_constant : (int, AD, int)
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, div_constant : (int, AD, int)
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, times : (int, AD, int, AD)
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}
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given clues : set of (AD, int, CLUE)
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$ clues
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such that
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forAll (targetKind, targetNum, clue) in clues .
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and(
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[ targetKind = A -> and(
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[ active(clue, is_constant) -> across[targetNum] = clue[is_constant]
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, active(clue, is_square ) -> exists i : number . i**2 = across[targetNum]
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, active(clue, is_prime ) -> and([ across[targetNum] % i != 0
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| i : number
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, i >= 2
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, i**2 <= across[targetNum]
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])
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, active(clue, plus_constant) -> and(
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[ clue[plus_constant ][2] = A -> across[targetNum] = across[clue[plus_constant ][1]] + clue[plus_constant ][3]
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, clue[plus_constant ][2] = D -> across[targetNum] = down [clue[plus_constant ][1]] + clue[plus_constant ][3]
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])
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, active(clue, minus_constant) -> and(
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[ clue[minus_constant][2] = A -> across[targetNum] = across[clue[minus_constant][1]] - clue[minus_constant][3]
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, clue[minus_constant][2] = D -> across[targetNum] = down [clue[minus_constant][1]] - clue[minus_constant][3]
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])
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, active(clue, times_constant) -> and(
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[ clue[times_constant][2] = A -> across[targetNum] = across[clue[times_constant][1]] * clue[times_constant][3]
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, clue[times_constant][2] = D -> across[targetNum] = down [clue[times_constant][1]] * clue[times_constant][3]
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])
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, active(clue, div_constant) -> and(
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[ clue[div_constant ][2] = A -> across[targetNum] = across[clue[div_constant ][1]] / clue[div_constant ][3]
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, clue[div_constant ][2] = D -> across[targetNum] = down [clue[div_constant ][1]] / clue[div_constant ][3]
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])
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, active(clue, times) -> and(
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[ (clue[times][2], clue[times][4]) = (A, A) -> across[targetNum] = across[clue[times][1]] * across[clue[times][3]]
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, (clue[times][2], clue[times][4]) = (A, D) -> across[targetNum] = across[clue[times][1]] * down [clue[times][3]]
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, (clue[times][2], clue[times][4]) = (D, A) -> across[targetNum] = down [clue[times][1]] * across[clue[times][3]]
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, (clue[times][2], clue[times][4]) = (D, D) -> across[targetNum] = down [clue[times][1]] * down [clue[times][3]]
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])
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])
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, targetKind = D -> and(
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[ active(clue, is_constant) -> down[targetNum] = clue[is_constant]
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, active(clue, is_square ) -> exists i : number . i**2 = down[targetNum]
21112

22-
forAll i : Clue . (
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l(i)[1] = Add ->
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grid[ l(i)[4,1], l(i)[4,2] ] =
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grid[ l( l(i)[2] )[4,1] , l( l(i)[2] )[4,2] ]
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+ grid[ l( l(i)[3] )[4,1] , l( l(i)[3] )[4,2] ] ) /\ (
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l(i)[1] = Modulo ->
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grid[ l(i)[4,1], l(i)[4,2] ] =
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grid[ l( l(i)[2] )[4,1] , l( l(i)[2] )[4,2] ]
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% grid[ l( l(i)[3] )[4,1] , l( l(i)[3] )[4,2] ]
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)
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, active(clue, is_prime ) -> and([ down[targetNum] % i != 0
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| i : number
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, i >= 2
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, i**2 <= down[targetNum]
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])
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, active(clue, plus_constant) -> and(
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[ clue[plus_constant ][2] = A -> down[targetNum] = across[clue[plus_constant ][1]] + clue[plus_constant ][3]
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, clue[plus_constant ][2] = D -> down[targetNum] = down [clue[plus_constant ][1]] + clue[plus_constant ][3]
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])
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, active(clue, minus_constant) -> and(
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[ clue[minus_constant][2] = A -> down[targetNum] = across[clue[minus_constant][1]] - clue[minus_constant][3]
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, clue[minus_constant][2] = D -> down[targetNum] = down [clue[minus_constant][1]] - clue[minus_constant][3]
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])
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, active(clue, times_constant) -> and(
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[ clue[times_constant][2] = A -> down[targetNum] = across[clue[times_constant][1]] * clue[times_constant][3]
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, clue[times_constant][2] = D -> down[targetNum] = down [clue[times_constant][1]] * clue[times_constant][3]
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])
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, active(clue, div_constant) -> and(
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[ clue[div_constant ][2] = A -> down[targetNum] = across[clue[div_constant ][1]] / clue[div_constant ][3]
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, clue[div_constant ][2] = D -> down[targetNum] = down [clue[div_constant ][1]] / clue[div_constant ][3]
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])
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, active(clue, times) -> and(
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[ (clue[times][2], clue[times][4]) = (A, A) -> down[targetNum] = across[clue[times][1]] * across[clue[times][3]]
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, (clue[times][2], clue[times][4]) = (A, D) -> down[targetNum] = across[clue[times][1]] * down [clue[times][3]]
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, (clue[times][2], clue[times][4]) = (D, A) -> down[targetNum] = down [clue[times][1]] * across[clue[times][3]]
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, (clue[times][2], clue[times][4]) = (D, D) -> down[targetNum] = down [clue[times][1]] * down [clue[times][3]]
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])
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])
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])

‎Problems/prob021/models/Crossfigures.essence.metadata

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---
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Title: The Essence model. Instance data can be found in the Essence Catalog.
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---

‎Problems/prob021/references/notes.inline.md

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11

2-
The problem appears in a list of puzzles maintained at cite{thinks_com}
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The problem appears in a list of puzzles maintained at cite{thinks_com}.
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The original website seems to have disappeared, but the referenced content is available at cite{thinks_com_wayback}.

‎Problems/prob021/references/references.bib

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howpublished = {\url{http://thinks.com/crosswords/xfig.htm}},
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}
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@misc{thinks_com_wayback,
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title = {Crossfigure Math Puzzles},
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howpublished = {\url{http://web.archive.org/web/20141017151205/http://thinks.com/crosswords/xfig.htm}},
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}
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