diff --git a/sudoku/sudoku.lua b/sudoku/sudoku.lua
index 1cd5217..344d2bf 100644
--- a/sudoku/sudoku.lua
+++ b/sudoku/sudoku.lua
@@ -1,8 +1,86 @@
-local utils = require "sudoku.utils"
+-- dbg = require ("debugger")
+-- dbg.auto_where = 2
 
-local sudoku = {}
+function table2string(t)
+    local myself = table2string
+    local l = {}
+    local n = 0
+    for k, v in pairs(t) do
+        n = n + 1
+        if type(v) == "table" then
+            l[n] = k .. ': ' .. myself(v)
+        elseif type(v) == "string" then
+            l[n] = k .. ': ' .. '"' .. v .. '"'
+        else
+            l[n] = k .. ': ' .. v
+        end
+    end
+    return "{" .. table.concat(l, ", ") .. "}"
+end
 
-function sudoku.iterZones(board)
+function find(array, element)
+    local index = 0
+    for i = 1, #array do
+        if array[i] == element then
+            index = i
+            break
+        end
+    end
+    return index
+end
+
+function createEmptyBoard()
+    local b = {}
+    for i = 1, 9 do
+        b[i] = {}
+        for j = 1, 9 do
+            b[i][j] = 0
+        end
+    end
+    return b
+end
+
+function cloneBoard(b)
+    local c = {}
+    for i = 1, 9 do
+        c[i] = {}
+        for j = 1, 9 do
+            c[i][j] = b[i][j]
+        end
+    end
+    return c
+end
+
+function loadBoard(fn)
+    local boards = {}
+    local r = 0
+    local board = {}
+    for line in io.lines(fn) do
+        if line:gsub("%s+", "") == "" then
+            table.insert(boards, board)
+            board = {}
+            r = 0
+        else
+            r = r + 1
+            local c = 0
+            board[r] = {}
+            for item in line:gmatch("%w+") do
+                c = c + 1
+                board[r][c] = tonumber(item)
+            end
+        end
+    end
+    table.insert(boards, board)
+    return boards
+end
+
+function showBoard(board)
+    for row = 1, 9 do
+        print(table.concat(board[row], " "))
+    end
+end
+
+function iterZones(board)
     local row = 0
     local column = 0
     local block = 0
@@ -44,7 +122,7 @@ function sudoku.iterZones(board)
     end
 end
 
-local function checkAUX(zone, pos)
+function checkAUX(zone, pos)
     local isComplete = true
     local ok = true
     local conflictList = {}
@@ -63,11 +141,11 @@ local function checkAUX(zone, pos)
     return ok, isComplete, conflictList
 end
 
-function sudoku.checkBoard(board)
+function checkBoard(board)
     local ok = true
     local isComplete = true
     local conflictList = {}
-    for zone, pos in sudoku.iterZones(board) do
+    for zone, pos in iterZones(board) do
         local tOk, tIsComplete, tConflictList = checkAUX(zone, pos)
         if not tOk then ok = false end
         if not tIsComplete then isComplete = false end
@@ -75,10 +153,11 @@ function sudoku.checkBoard(board)
             table.insert(conflictList, conflict)
         end
     end
+    if not ok then isComplete = false end
     return ok, isComplete, conflictList
 end
 
-function sudoku.calCellValidOptions(board, x, y)
+function calCellValidOptions(board, x, y)
     if board[x][y] ~= 0 then return {} end
     local u = {}
     local v = {}
@@ -104,19 +183,360 @@ function sudoku.calCellValidOptions(board, x, y)
     return v
 end
 
-function sudoku.buildSearchSpace(board)
+function buildSearchSpace(board)
     local s = {}
     for i = 1, 9 do
         s[i] = {}
         for j = 1, 9 do
-            s[i][j] = sudoku.calCellValidOptions(board, i, j)
+            s[i][j] = calCellValidOptions(board, i, j)
         end
     end
     return s
 end
 
-sudoku.cloneBoard = utils.cloneBoard
-sudoku.createEmptyBoard = utils.createEmptyBoard
-sudoku.loadBoard = utils.loadBoard
-return sudoku
+function findPairsIndSearchSpace(board, searchSpace)
+    local r = {}
+    local zoneIndex = 0
+    for zone, pos in iterZones(board) do
+        zoneIndex = zoneIndex + 1
+        for i = 1, 8 do
+            local x1 = pos[i][1]
+            local y1 = pos[i][2]
+            local s1 = searchSpace[x1][y1]
+            if #s1 == 2 then
+                for j = i + 1, 9 do
+                    local x2 = pos[j][1]
+                    local y2 = pos[j][2]
+                    local s2 = searchSpace[x2][y2]
+                    if #s2 == 2 then
+                        if s1[1] == s2[1] and s1[2] == s2[2] then
+                            -- if zoneIndex <= 18 or x1 ~= x2 and y1 ~= y2 then
+                            table.insert(r, {zoneIndex=zoneIndex, cells={i, j}, pair=s1})
+                                -- print("----------")
+                                -- print("zone: ", zoneIndex)
+                                -- print(table2string(zone))
+                                -- print(i, j)
+                                -- print(table2string(s1))
+                            -- end
+                        end
+                    end
+                end
+            end
+        end
+    end
+    return r
+end
 
+function showSearchSpace(s)
+    local hl = ("+-------+-------+-------+-------+-------+-------+-------+-------+-------+")
+    print(hl)
+    for i = 1, 27 do
+        local x = math.floor((i - 1) / 3) + 1
+        local a = (i - 1) % 3
+        local row = {}
+        for j = 1, 27 do
+            local y = math.floor((j - 1) / 3) + 1
+            local k = ((j - 1) % 3 + 1) + 3 * a
+            local found = false
+            for _, m in ipairs(s[x][y]) do
+                if m == k then found = true; break end
+            end
+            if found then
+                table.insert(row, k)
+            else
+                table.insert(row, " ")
+            end
+            if j % 3 == 0 then table.insert(row, "|") end
+        end
+        print("| "..table.concat(row, " "))
+        if i % 3 == 0 then print(hl) end
+    end
+end
+
+function getZoneByIndex(board, zoneIndex)
+    local index = (zoneIndex - 1) % 9 + 1
+    local block = math.floor((zoneIndex - 1) / 9) + 1
+    local a = {}
+    local p = {}
+    if block == 1 then
+        for i = 1, 9 do
+            a[i] = board[index][i]
+            p[i] = {index, i}
+        end
+    elseif block == 2 then
+        for i = 1, 9 do
+            a[i] = board[i][index]
+            p[i] = {index, i}
+        end
+    elseif block == 3 then
+        local dx = math.floor((index - 1) / 3)
+        local dy = (index - 1) % 3
+        local n = 0
+        for i = 1, 3 do
+            for j = 1, 3 do
+                local x = i + 3 * dx
+                local y = j + 3 * dy
+                n = n + 1
+                a[n] = board[x][y]
+                p[n] = {x, y}
+            end
+        end
+    end
+    return a, p
+end
+
+function getZonePosByIndex(zoneIndex)
+    local index = (zoneIndex - 1) % 9 + 1
+    local block = math.floor((zoneIndex - 1) / 9) + 1
+    local p = {}
+    if block == 1 then
+        for i = 1, 9 do
+            p[i] = {index, i}
+        end
+    elseif block == 2 then
+        for i = 1, 9 do
+            p[i] = {index, i}
+        end
+    elseif block == 3 then
+        local dx = math.floor((index - 1) / 3)
+        local dy = (index - 1) % 3
+        local n = 0
+        for i = 1, 3 do
+            for j = 1, 3 do
+                local x = i + 3 * dx
+                local y = j + 3 * dy
+                n = n + 1
+                p[n] = {x, y}
+            end
+        end
+    end
+    return p
+end
+
+function iterZonePos(zoneIndex)
+    local p = getZonePosByIndex(zoneIndex)
+    local i = 0
+    return function()
+        if i < 9 then
+            i = i + 1
+            return p[i][1], p[i][2]
+        end
+    end
+end
+
+function fillSingles(board, searchSpace)
+    local count = 0
+    for i = 1, 9 do
+        for j = 1, 9 do
+            if #searchSpace[i][j] == 1 then
+                board[i][j] = searchSpace[i][j][1]
+                count = count + 1
+            end
+        end
+    end
+    return count
+end
+
+function applyFillSinglesRepeatedly(board, s)
+    local s = s or buildSearchSpace(board)
+    local count = fillSingles(board, s)
+    local total = count
+    while count ~= 0 do
+        s = buildSearchSpace(board)
+        count = fillSingles(board, s)
+        total = total + count
+    end
+    return total
+end
+
+function eliminatePairsInSearchSpaceAUX(board, searchSpace, pair, zoneIndex, cells)
+    local _, pos = getZoneByIndex(board, zoneIndex)
+    local count = 0
+    for i = 1, 9 do
+        if i ~= cells[1] and i ~= cells[2] then
+            local x = pos[i][1]
+            local y = pos[i][2]
+            local del = {}
+            for index, v in ipairs(searchSpace[x][y]) do
+                if v == pair[1] or v == pair[2] then
+                    count = count + 1
+                    table.insert(del, index)
+                end
+            end
+            for _, index in ipairs(del) do
+                table.remove(searchSpace[x][y], index)
+            end
+        end
+    end
+    return count
+end
+
+function eliminatePairsInSearchSpace(board, searchSpace)
+    local p = findPairsIndSearchSpace(board, searchSpace)
+    local count = 0
+    for _, m in ipairs(p) do
+        count = count + eliminatePairsInSearchSpaceAUX(board, searchSpace, m.pair, m.zoneIndex, m.cells)
+    end
+    return count
+end
+
+function allPairs(board)
+    local s = buildSearchSpace(board)
+    applyFillSinglesRepeatedly(board, s)
+    eliminatePairsInSearchSpace(board, s)
+    local count = applyFillSinglesRepeatedly(board, s)
+    while count ~= 0 do
+        -- print("--------------------------------------------------")
+        -- showBoard(board)
+        -- showSearchSpace(s)
+        -- print(count)
+        -- io.read(1)
+        s = buildSearchSpace(board)
+        eliminatePairsInSearchSpace(board, s)
+        count = applyFillSinglesRepeatedly(board, s)
+    end
+end
+
+function findFirstEmptyCell(board)
+    for i = 1, 9 do
+        for j = 1, 9 do
+            if board[i][j] == 0 then
+                return i, j
+            end
+        end
+    end
+end
+
+function checkSearchSpace(board, searchSpace)
+    local s = searchSpace or buildSearchSpace(board)
+    for i = 1, 9 do
+        for j = 1, 9 do
+            if board[i][j] == 0 then
+                if #s[i][j] == 0 then return false end
+            end
+        end
+    end
+    return true
+end
+
+function backTrace2(board, s)
+    local s = s or buildSearchSpace(board)
+    local x, y = findFirstEmptyCell(board)
+    for _, v in ipairs(s[x][y]) do
+        local b = cloneBoard(board)
+        b[x][y] = v
+        allPairs(b)
+        local ok, finished = checkBoard(b)
+        if finished then return b end
+        if ok and checkSearchSpace(b) then
+            local r = backTrace(b)
+            if r then return r end
+        end
+    end
+end
+
+function backTrace3(board, tried)
+    -- dbg()
+    local tried = tried or createEmptyBoard()
+    for x = 1, 9 do
+        for y = 1, 9 do
+            if tried[x][y] == 0 and board[x][y] == 0 then
+                tried[x][y] = 1
+                print(x, y)
+                local s = buildSearchSpace(board)
+                for _, v in ipairs(s[x][y]) do
+                    local b = cloneBoard(board)
+                    b[x][y] = v
+                    allPairs(b)
+                    local ok, finished = checkBoard(b)
+                    if finished then return b end
+                    if ok and checkSearchSpace(b) then
+                        local r = backTrace(b, tried)
+                        if r then return r end
+                    end
+                end
+            end
+        end
+    end
+end
+
+function backTrace4(board, cx, cy)
+    local s = buildSearchSpace(board)
+    for x = 1, 9 do
+        for y = 1, 9 do
+            if x ~= cx and y ~=cy then
+                for _, v in ipairs(s[x][y]) do
+                    local b= cloneBoard(board)
+                    b[x][y] = v
+                    print(x, y, v)
+                    -- allPairs(b)
+                    applyFillSinglesRepeatedly(b)
+                    local ok, finished = checkBoard(b)
+                    if finished then return b end
+                    if ok and checkSearchSpace(b) then
+                        local r = backTrace(b, x, y)
+                        if r then return r end
+                    end
+                end
+            end
+        end
+    end
+end
+
+function backTrace(board)
+    local s = buildSearchSpace(board)
+    for x = 1, 9 do
+        for y = 1, 9 do
+            for _, v in ipairs(s[x][y]) do
+                local b= cloneBoard(board)
+                b[x][y] = v
+                -- allPairs(b)
+                applyFillSinglesRepeatedly(b)
+                local ok, finished = checkBoard(b)
+                print(x, y, v, ok, finished)
+                showBoard(b)
+                io.read(1)
+                if finished then return b end
+                if ok and checkSearchSpace(b) then
+                    local r = backTrace(b, x, y)
+                    if r then return r end
+                end
+            end
+            return
+        end
+    end
+end
+
+function solve(board)
+    -- allPairs(board)
+    applyFillSinglesRepeatedly(board)
+    local ok, finished = checkBoard(board)
+    if not ok then print("something's wrong!"); return end
+    if finished then showBoard(board); return end
+    local r = backTrace(board)
+    if r then
+        showBoard(r)
+    else
+        print "Could not solve!"
+    end
+end
+
+function sHelper(n)
+    local fn = string.format("/home/reza/p/lua/22.sudoku/boards/%03d.txt", n)
+    local board = loadBoard(fn)[1]
+    solve(board)
+end
+
+-- b = loadBoard("b.txt")[1]
+-- applyFillSinglesRepeatedly(b)
+-- s = buildSearchSpace(b)
+-- allPairs(b)
+
+
+return {
+    loadBoard = loadBoard,
+    calCellValidOptions = calCellValidOptions,
+    cloneBoard = cloneBoard,
+    checkBoard = checkBoard,
+    createEmptyBoard = createEmptyBoard,
+}
diff --git a/sudoku/utils.lua b/sudoku/utils.lua
deleted file mode 100644
index e9937b6..0000000
--- a/sudoku/utils.lua
+++ /dev/null
@@ -1,84 +0,0 @@
-local function table2string(t)
-    local myself = table2string
-    local l = {}
-    local n = 0
-    for k, v in pairs(t) do
-        n = n + 1
-        if type(v) == "table" then
-            l[n] = k .. ': ' .. myself(v)
-        elseif type(v) == "string" then
-            l[n] = k .. ': ' .. '"' .. v .. '"'
-        else
-            l[n] = k .. ': ' .. v
-        end
-    end
-    return "{" .. table.concat(l, ", ") .. "}"
-end
-
-local function find(array, element)
-    local index = 0
-    for i = 1, #array do
-        if array[i] == element then
-            index = i
-            break
-        end
-    end
-    return index
-end
-
-local function createEmptyBoard()
-    local b = {}
-    for i = 1, 9 do
-        b[i] = {}
-        for j = 1, 9 do
-            b[i][j] = 0
-        end
-    end
-    return b
-end
-
-local function cloneBoard(b)
-    local c = {}
-    for i = 1, 9 do
-        c[i] = {}
-        for j = 1, 9 do
-            c[i][j] = b[i][j]
-        end
-    end
-    return c
-end
-
-local function loadBoard(fn)
-    local boards = {}
-    local r = 0
-    local board = {}
-    for line in io.lines(fn) do
-        if line:gsub("%s+", "") == "" then
-            table.insert(boards, board)
-            board = {}
-            r = 0
-        else
-            r = r + 1
-            local c = 0
-            board[r] = {}
-            for item in line:gmatch("%w+") do
-                c = c + 1
-                board[r][c] = tonumber(item)
-            end
-        end
-    end
-    table.insert(boards, board)
-    return boards
-end
-
-local function showBoard(board)
-    for row = 1, 9 do
-        print(table.concat(board[row], " "))
-    end
-end
-
-return {
-    createEmptyBoard = createEmptyBoard,
-    cloneBoard = cloneBoard,
-    loadBoard = loadBoard,
-}