Version 6 of TkChallenger
Updated 2002-10-15 18:25:03Keith Vetter - Here's a little tk program that lets you solve the Challenger puzzles that you often find syndicated in the daily paper [L1 ]. In this puzzle you must make each row, column and diagonal add up to a certain sum. This program aids in solving them by giving you running totals, showing illegal, correct and forced squares.
I wrote it with the intention that the user would enter the day's puzzle and then solve it. But I've also include a half-dozen or so puzzles from the last week to give you a taste.
KBK Lovely! Now to do an auto-solver, too, since Tcl is good at Solving cryptarithms and this sort of puzzle is amenable to similar techniques...
KPV Actually I already wrote one a long time ago, I'll see if I can dig it out. I used a brute force guessing solution, but if I remember correctly, if you are smart in which squares to guess first, you only have to guess about four squares before everything gets forced.
KPV You asked and you shall get. This version has a "solve" button. It generates code on the fly to do a brute-force search to solve the first two rows, after which everything is forced. This requires at most 6,561 (9^4) guesses.
##+##########################################################################
#
# challenger.tcl
#
# Challenger -- helps solve the challenger math puzzle
# by Keith Vetter
#
# Revisions:
# KPV Oct 08, 2002 - initial revision
# KPV Oct 14, 2002 - added auto solve
#
##+##########################################################################
#############################################################################
# All the cells in the puzzle
set state(cells) { 0 4
1 0 1 1 1 2 1 3 1 4
2 0 2 1 2 2 2 3 2 4
3 0 3 1 3 2 3 3 3 4
4 0 4 1 4 2 4 3 4 4
5 0 5 1 5 2 5 3 5 4 }
# Some puzzles to play with
set puzzle(0) {16 . 1 . . 9 . . . 3 16 . . 2 . 17 1 . . . 9 11 18 12 10 12}
set puzzle(1) {24 . . 3 . 14 . 9 . . 34 . . . 7 33 6 . . . 30 28 27 29 27 32}
set puzzle(2) {18 . . 3 . 10 . 4 . . 20 . . . 1 10 5 . . . 20 12 13 17 18 12}
set puzzle(3) {7 . 1 . . 8 . . . 1 9 . . 1 . 10 1 . . . 11 9 9 9 11 12}
set puzzle(4) {23 . . . 5 23 6 . . . 23 . . 6 . 23 . 5 . . 23 25 19 25 23 23}
set puzzle(5) {33 . 9 . . 28 . . . 6 30 . . 8 . 29 8 . . . 30 29 30 32 26 27}
set puzzle(6) {35 . . 5 . 23 . 2 . . 21 . . . 9 20 8 . . . 31 20 24 20 31 17}
set puzzle(7) {28 . 9 . . 26 . . 5 . 26 8 . . . 27 . . . 5 27 30 30 22 24 25}
set puzzle(8) {15 5 . . . 16 . . . 3 6 . 3 . . 22 . . 4 . 15 21 12 7 19 9}
set puzzle(9) {23 . . . 9 19 . 4 . . 11 7 . . . 15 . . 8 . 35 22 18 20 20 21}
set puzzle(10) {9 2 . . . 8 . . 4 . 10 . . . 2 11 . 3 . . 15 10 6 14 14 16}
set puzzle(11) {29 . . 8 . 30 2 . . . 22 . 6 . . 32 . . . 9 31 25 27 32 31 33}
# The rows, columns and diagonals
array set rows {
1,4 {1,0 1,1 1,2 1,3} 2,4 {2,0 2,1 2,2 2,3} 3,4 {3,0 3,1 3,2 3,3}
4,4 {4,0 4,1 4,2 4,3} 5,0 {1,0 2,0 3,0 4,0} 5,1 {1,1 2,1 3,1 4,1}
5,2 {1,2 2,2 3,2 4,2} 5,3 {1,3 2,3 3,3 4,3} 5,4 {1,0 2,1 3,2 4,3}
0,4 {4,0 3,1 2,2 1,3}
}
array set move {Up {-1 0} Down {1 0} Left {0 -1} Right {0 1}}
set state(locked) 0
set state(undo) {}
set state(forced) {}
set state(who) -1
proc DoDisplay {} {
wm title . "TkChallenger"
DoMenus
frame .play -bd 2 -relief raised -padx 30 -pady 0
frame .play.tm -height 20
grid .play.tm
frame .bottom
for {set row 0} {$row < 6} {incr row} {
set cells {}
if {$row == 0} {set cells "x x x x"}
for {set col 0} {$col < 5} {incr col} {
if {$row == 0} {set col 4}
set tag ".e$row,$col"
entry $tag -width 6 -textvariable ss($row,$col) -justify c \
-disabledbackground lightblue -exportselection 0
$tag config -disabledforeground [$tag cget -foreground]
bind $tag <Key> [list MyKey %W %A %K]
if {$row == 5 || $col == 4} {
$tag config -bg cyan -disabledbackground cyan
}
lappend cells $tag
}
eval grid $cells -in .play -sticky we
}
label .msg -anchor w -bg [.play cget -bg] -textvariable state(msg)
grid .msg - - - - -in .play -sticky ew -pady 5
button .forced -text "Do Forced Moves" -command DoForced -takefocus 0
button .undo -text Undo -command Undo -state disabled -takefocus 0
button .solve -text Solve -command Solve -takefocus 0
pack .play .bottom -side top -fill both -expand 1
pack .solve .forced .undo -in .bottom -side left -pady 10 -expand 1
array set ::b2m {.lock {.m.puzzle 4} .unlock {.m.puzzle 5} .undo {.m.edit 4}
.erase {.m.edit 0} .eraseA {.m.edit 1} .forced {.m.edit 3}
.solve {.m.puzzle 7}
}
focus .e1,0
DoButtons
}
proc DoMenus {} {
menu .m -tearoff 0
. configure -menu .m ;# Attach menu to main window
# Top level menu buttons
.m add cascade -menu .m.puzzle -label "Puzzle" -underline 0
.m add cascade -menu .m.edit -label "Edit" -underline 0
.m add cascade -menu .m.help -label "Help" -underline 0
menu .m.puzzle -tearoff 0
.m.puzzle add command -label "Reset Puzzle" -under 0 \
-command {PickPuzzle -1}
.m.puzzle add command -label "Blank Puzzle" -under 0 -command {Erase 1}
.m.puzzle add command -label "New Puzzle" -under 0 -command PickPuzzle
.m.puzzle add separator
.m.puzzle add command -label "Lock Puzzle" -under 0 -command Lock
.m.puzzle add command -label "Unlock Puzzle" -under 0 -command Unlock
.m.puzzle add separator
.m.puzzle add command -label Solve -under 0 -command Solve
.m.puzzle add separator
.m.puzzle add command -label Exit -under 0 -command exit
menu .m.edit -tearoff 0
.m.edit add command -label "Erase" -under 0 -command {Erase 0}
.m.edit add command -label "Erase All" -under 6 -command {Erase 1}
.m.edit add separator
.m.edit add command -label "Do Forced Moves" -under 0 -command DoForced
.m.edit add command -label "Undo" -under 0 -command Undo
menu .m.help -tearoff 0
.m.help add command -label Help -under 0 -command Help
}
proc INFO {msg} { set ::state(msg) $msg ; update}
proc PickPuzzle {{who ""}} {
global state ss puzzle
if {$who == ""} { ;# Pick one at random
set names [array names puzzle]
set len [llength $names]
while {1} {
set n [expr {int(rand() * $len)}]
set who [lindex $names $n]
if {$who != $state(who)} break
if {$len == 1} break
}
} elseif {$who == -1} {
set who $state(who)
}
if {! [info exists puzzle($who)]} {
Erase 0
return
}
Erase 1
set state(who) $who
foreach {row col} $state(cells) val $puzzle($who) {
if {$val == "."} {set val {}}
set ss($row,$col) $val
}
Lock
INFO "Puzzle #$who"
}
# DoButtons -- set the buttons state depending on circumstances
proc DoButtons {} {
global state b2m
array set s {1 normal 0 disabled}
set ww [list .lock .unlock .erase .eraseA .solve .undo .forced]
# Get into bb the states we want
if {$state(locked)} { set bb {0 1 1 0 1} } { set bb {1 0 0 1 0} }
lappend bb [expr {[llength $state(undo)] > 0 ? 1 : 0}]
lappend bb [expr {[llength $state(forced)] > 0 ? 1 : 0}]
foreach w $ww b $bb {
if {[winfo exists $w]} { ;# Configure the button
$w configure -state $s($b)
}
foreach {m e} $::b2m($w) { ;# Configure the menu
$m entryconfigure $e -state $s($b)
}
}
}
# Lock -- locks (by disabling) all cells w/ values in them
proc Lock {} {
global ss state
foreach {row col} $state(cells) {
set tag ".e$row,$col"
if {$row == 5 || $col == 4} {
append ss($row,$col) "/ "
} elseif {$ss($row,$col) == ""} continue
$tag config -state disabled
}
set state(locked) 1
set state(undo) {}
DoButtons
SumRows
set w [focus -lastfor .]
catch {
if {[$w cget -state] != "normal"} {
event generate $w <Tab>
}
}
}
# Unlock -- unlocks (by enabling) all cells
proc Unlock {} {
global ss state
foreach {row col} $state(cells) {
set tag ".e$row,$col"
$tag config -state normal
if {$row == 5 || $col == 4} {
regsub {/.*} $ss($row,$col) {} ss($row,$col)
}
}
set state(locked) 0
DoButtons
}
# Erase -- erases either all non-locked cells, or all cells
proc Erase {all} {
if {! $all && $::state(locked) == 0} return
set undo {}
foreach {row col} $::state(cells) {
set tag ".e$row,$col"
if {$all || [$tag cget -state] == "normal"} {
set was [$tag get]
lappend undo $tag "$row,$col" $was
set ::ss($row,$col) ""
}
}
SumRows
lappend ::state(undo) $undo
if {$all} {
INFO ""
Unlock
set ::state(who) "user"
}
focus .e1,0
DoButtons
}
proc GetPuzzle {} {
global state ss
set p ""
foreach {row col} $state(cells) {
set val $ss($row,$col)
if {$val == ""} {set val .}
regsub {/.*} $val "" val
append p "$val "
}
return [string trim $p]
}
# SumRows -- the workhorse of our program. Sums up each row and
# updates the running total (deficit actually) and does cell
# configuring for bad, good and forced cells.
proc SumRows {} {
global state ss
if {$::state(locked) == 0} { return 0}
foreach {row col} $state(cells) { ;# Put all cells back to white
set tag ".e$row,$col"
if {[$tag cget -state] == "normal"} { $tag config -bg white }
if {$row == 5 || $col == 4} { $tag config -disabledbackground cyan }
}
_SumRows ss
foreach cell $state(good) {
.e$cell config -disabledbackground green
}
foreach cell $state(bad) {
.e$cell config -disabledbackground red
}
foreach {cell value} $state(forced) {
.e$cell config -background yellow
}
DoButtons
if {[llength $state(good)] == 10} { return 1 } ;# Solved
if {[llength $state(bad)] != 0} { return -1 } ;# Bad
return 0
}
proc _SumRows {_SS} {
global rows state
upvar 1 $_SS SS
set state(forced) {}
set state(bad) {}
set state(good) {}
foreach scell [array names rows] { ;# Loop on each row/col/diagonal
set n [regexp {\s*([0-9]+)/?} $SS($scell) => max]
if {! $n} continue
set sum 0
set missing {}
foreach cell $rows($scell) { ;# Each cell in row/col/diag
set val $SS($cell)
if {[string is integer -strict $val]} {
set sum [expr {$sum + $val}]
} else {
lappend missing $cell
}
}
# Show running deficit
set SS($scell) [format "%2d/%2d" $max [expr {$max - $sum}]]
set SS(d,$scell) [expr {$max - $sum}]
# Figure out bad, good or forced cells stuff
set num [llength $missing]
if {$num == 0 && $sum == $max} {
lappend state(good) $scell
} elseif {$num == 0 || $sum > $max} {
lappend state(bad) $scell
} else {
set delta [expr {1.0 * ($max - $sum) / $num}]
if {$delta < 1 || $delta > 9} {
lappend state(bad) $scell
} elseif {$num == 1 || $delta == 1.0 || $delta == 9.0} {
foreach who $missing {
lappend state(forced) $who [expr {int($delta)}]
}
}
}
}
}
proc IsSolved {} {
return [expr {[llength $::state(good)] == 10 ? 1 : 0}]
}
# DoForced -- fills in the values for all forced cells
proc DoForced {{repeat 0}} {
global state ss
set undo {} ;# So we can undo this action
while {[llength $state(forced)] > 0} {
catch {unset done}
foreach {cell val} $state(forced) {
if {[info exists done($cell)]} continue
lappend undo ".e$cell" $cell $ss($cell)
set ss($cell) $val
set done($cell) $val
}
lappend state(undo) $undo
SumRows
if {! $repeat} break
}
}
proc _DoForced {_SS} {
global state
upvar 1 $_SS SS
_SumRows SS
while {[llength $state(forced)] > 0} {
foreach {cell val} $state(forced) {
set SS($cell) $val
}
_SumRows SS
if {[llength $state(bad)] > 0} { return -1 }
}
if {[llength $state(good)] == 10} { return 1 } ;# Solved
if {[llength $state(bad)] != 0} { return -1 } ;# Bad
return 0
}
# MyKey -- handles all keystrokes for each cell
proc MyKey {w char sym} {
regexp {([0-9]),([0-9])} $w who row col
set before [$w get] ;# For undo info
switch -- $sym {
"Tab" { return -code continue }
"asterisk" { Undo }
z { if {$char == "\x1A"} Undo }
"space" { $w delete 0 end }
"BackSpace" - "Delete" {
set pos [$w index insert]
$w delete [incr pos -1] end
}
"Home" - "End" {
if {$sym == "End"} {set event <Shift-Tab>} {set event <Tab>}
focus .e0,4 ; event generate .e0,4 $event
}
"Up" - "Down" - "Left" - "Right" {
foreach {drow dcol} $::move($sym) break
while {1} {
incr row $drow ; incr col $dcol
set ww ".e$row,$col"
if {! [winfo exists $ww]} {return -code break}
if {[$ww cget -state] != "normal"} continue
focus $ww
break
}
}
default {
if {! [string is integer -strict $char]} { return -code break }
if {$row == 5 || $col == 4} { ;# Sum cells
set val [$w get]
if {$val != ""} {
set char [expr {(($val * 10) + $char) % 100}]
}
} elseif {$char == "0"} {
set char ""
}
$w delete 0 end
$w insert 0 $char
#$w selection range 0 end
$w icursor end
if {$row < 5 && $col < 4} {
event generate $w <Tab> ;# Move to next cell
}
}
}
set now [$w get]
if {$before != $now} {lappend ::state(undo) [list $w $who $before]}
SumRows
return -code break
}
# Undo -- Undoes the last operation
proc Undo {} {
global state ss
# Pop off the event to undo
set item [lindex $state(undo) end]
set state(undo) [lrange $state(undo) 0 end-1]
foreach {w who was} $item {
set ss($who) $was
focus $w
}
SumRows
DoButtons
}
proc Help {} {
catch {destroy .help}
toplevel .help
wm title .help "TkChallenger Help"
wm geom .help "+[expr {[winfo x .] + [winfo width .] + 10}]+[winfo y .]"
text .help.t -relief raised -wrap word -width 70 -height 34
.help.t config -padx 10 -pady 10
button .help.dismiss -text Dismiss -command {destroy .help}
pack .help.t -side top -expand 1 -fill both
pack .help.dismiss -side bottom -expand 1 -pady 10
set bold "[font actual [.help.t cget -font]] -weight bold"
.help.t tag configure title -justify center -foreground red \
-font "Times 20 bold"
.help.t tag configure title2 -justify center -font "Times 12 bold"
.help.t tag configure bullet -font $bold
.help.t tag configure bn -lmargin1 15 -lmargin2 15
.help.t tag configure bn2 -lmargin1 15 -lmargin2 20
.help.t insert end "TkChallenger\n" title
.help.t insert end "by Keith Vetter\n\n" title2
set m "This program helps you solve the Challenger puzzles that you often "
append m "see in the daily paper. I wrote this program because I'm "
append m "horrible at solving these puzzles--this helps but I'm still bad."
.help.t insert end $m n \n\n
.help.t insert end "How to Play" bullet \n
set m "Fill in each square with a number, 1-9. "
append m "Horizontal square should add to the total on "
append m "the right, vertical squares to the number on the "
append m "bottom and the main diagonals to the number in "
append m "the upper and lower right."
.help.t insert end $m bn \n\n
.help.t insert end "What the Different Colored Squares Mean" bullet \n
set m "- Cyan squares show the value each row or column must add up "
append m "to along with the amount still needed to reach that value.\n"
append m "- Light blue squares are playing squares with known values.\n"
append m "- Green squares show when a row or column is correct.\n"
append m "- Red squares show when a row or column is in an illegal state.\n"
append m "- Yellow squares show squares for which the value is forced."
.help.t insert end $m bn2 \n\n
.help.t insert end "Built in Puzzles" bullet \n
set m "TkChallenger comes with about half-a-dozen built in puzzles, "
append m "but is really designed for you to create your own. "
append m "Unlocking the puzzle allows you to enter values into "
append m "any square. Once you've entered the puzzle, lock it and "
append m "solve away."
.help.t insert end $m bn \n\n
.help.t insert end "Auto Solve" bullet \n
set m "TkChallenge can solve the puzzle for you. It does a brute "
append m "force search trying all possibilities for the top two "
append m "rows, after which the remaining squares are usually forced. "
append m "This requires at most 6,561 (9^4) guesses for the typical "
append m "published Challenger puzzle that has 4 squares already filled "
append m "in."
.help.t insert end $m bn \n\n
.help.t config -state disabled
}
proc Solve {} {
INFO "searching for solution..."
DoForced ;# Fill all forced cells
set start [clock click -milliseconds]
set code [GenerateCode] ;# This code will solve it
eval $code
foreach {solved cnt} [solvex] break
set start [expr {([clock click -milliseconds] - $start)/1000.0}]
set guesses "guess" ; if {$cnt != 1} {set guesses guesses}
if {$solved} {
INFO "Solved: $start sec and $cnt $guesses"
set ::state(undo) {}
} else {
INFO "No solution: $start sec and $cnt $guesses"
}
DoButtons
}
proc GenerateCode {} {
set braces 0
set code "proc solvex {} \{\n set cnt 0\n"
append code " array set SS \[array get ::ss]\n\n"
set indent 1
foreach row {1 2} {
foreach {b code2} [GenCodeRow $row [string repeat " " $indent]] {
incr braces $b
append code $code2 "\n"
incr indent $b
}
}
set ind [string repeat " " $indent]
append code $ind "set save \[array get SS]\n"
append code $ind "incr cnt\n"
append code $ind "set n \[_DoForced SS]\n"
append code $ind "if {\$n == 1} \{\n"
append code $ind " array set ::ss \[array get SS]\n"
append code $ind " SumRows\n"
append code $ind " return \[list 1 \$cnt]\n"
append code $ind "\}\n"
append code $ind "array set SS \$save\n"
append code [string repeat "\}\n" $braces]
append code " return \[list 0 \$cnt]\n"
append code "\}"
return $code
}
proc GenCodeRow {row indent} {
global ss
set missing {}
foreach col {0 1 2 3} {
if {$ss($row,$col) == {}} { lappend missing "SS($row,$col)" }
}
set num [llength $missing]
if {$num == 0} {
return [list 0 "$indent; # complete row\n"]
}
set last [lindex $missing end]
set code ""
set code2 "set $last \[expr {$ss(d,$row,4)"
for {set i 0} {$i < $num-1} {incr i} {
set cell [lindex $missing $i]
append code $indent
append indent " "
append code "for {set $cell 1} {\$$cell < 10} {incr $cell} \{\n"
append code2 " - \$$cell"
}
append code $indent $code2 "}]\n"
append code $indent "if {\$$last < 1 || \$$last > 9} continue\n"
return [list [incr num -1] $code]
}
################################################################
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DoDisplay
PickPuzzle