diff --git a/meson.build b/meson.build
index ef8e833..0dc7f4e 100644
--- a/meson.build
+++ b/meson.build
@@ -11,11 +11,18 @@ project(
 sources = [
   'src/constraints.c',
   'src/main.c',
+  'src/solver/solve.c',
+  'src/solver/update_sets.c',
   'src/sudoku.c',
 ]
 
+incdir = include_directories(
+  'src',
+)
+
 executable(
   'sudoku',
   sources : sources,
   c_args : '-D_POSIX_C_SOURCE=200809L',
+  include_directories : incdir,
 )
diff --git a/src/solver/internals.h b/src/solver/internals.h
new file mode 100644
index 0000000..0ebba42
--- /dev/null
+++ b/src/solver/internals.h
@@ -0,0 +1,10 @@
+#ifndef INTERNALS_H
+#define INTERNALS_H
+
+#include <stdbool.h>
+
+struct sudoku;
+
+bool update_sets(const struct sudoku *grid, bool possibilities[9][9][9]);
+
+#endif /* !INTERNALS_H */
diff --git a/src/solver/solve.c b/src/solver/solve.c
new file mode 100644
index 0000000..15125ea
--- /dev/null
+++ b/src/solver/solve.c
@@ -0,0 +1,34 @@
+#include "solve.h"
+
+#include <stddef.h>
+
+#include "constraints.h"
+#include "internals.h"
+#include "sudoku.h"
+
+static void init_possibilities(bool possibilities[9][9][9]) {
+    for (size_t i = 0; i < 9; ++i) {
+        for (size_t j = 0; j < 9; ++j) {
+            for (size_t n = 0; n < 9; ++n) {
+                possibilities[i][j][n] = true;
+            }
+        }
+    }
+}
+
+bool solve(struct sudoku *grid) {
+    if (!grid)
+        return false;
+
+    bool possibilities[9][9][9];
+    init_possibilities(possibilities);
+
+    bool changed;
+    do {
+        changed = false;
+
+        changed |= update_sets(grid, possibilities);
+    } while (changed);
+
+    return solved(grid);
+}
diff --git a/src/solver/solve.h b/src/solver/solve.h
new file mode 100644
index 0000000..0f3028c
--- /dev/null
+++ b/src/solver/solve.h
@@ -0,0 +1,10 @@
+#ifndef SOLVE_H
+#define SOLVE_H
+
+#include <stdbool.h>
+
+struct sudoku;
+
+bool solve(struct sudoku *grid);
+
+#endif /* !SOLVE_H */
diff --git a/src/solver/update_sets.c b/src/solver/update_sets.c
new file mode 100644
index 0000000..e550fa9
--- /dev/null
+++ b/src/solver/update_sets.c
@@ -0,0 +1,85 @@
+#include "internals.h"
+
+#include <stddef.h>
+
+#include "sudoku.h"
+
+static bool ensure_unique(bool possibilities[9][9][9], size_t i, size_t j,
+                          int num) {
+    bool changed = false;
+
+    for (int n = 0; n < 9; ++n) {
+        if (n == num)
+            continue;
+        changed |= possibilities[i][j][n];
+        possibilities[i][j][n] = false;
+    }
+
+    return changed;
+}
+
+static bool update_line(bool possibilities[9][9][9], size_t i, size_t j,
+                        int num) {
+    bool changed = false;
+
+    for (size_t c = 0; c < 9; ++c) {
+        if (c == j)
+            continue;
+        changed |= possibilities[i][c][num];
+        possibilities[i][c][num] = false;
+    }
+
+    return changed;
+}
+
+static bool update_column(bool possibilities[9][9][9], size_t i, size_t j,
+                          int num) {
+    bool changed = false;
+
+    for (size_t l = 0; l < 9; ++l) {
+        if (l == i)
+            continue;
+        changed |= possibilities[l][j][num];
+        possibilities[l][j][num] = false;
+    }
+
+    return changed;
+}
+
+static bool update_square(bool possibilities[9][9][9], size_t i, size_t j,
+                          int num) {
+    bool changed = false;
+
+    const size_t x = i / 3;
+    const size_t y = j / 3;
+
+    for (size_t l = 3 * x; l < 3 * (x + 1); ++l) {
+        for (size_t c = 3 * y; c < 3 * (y + 1); ++c) {
+            if (l == i && c == j)
+                continue;
+            changed |= possibilities[l][c][num];
+            possibilities[l][c][num] = false;
+        }
+    }
+
+    return changed;
+}
+
+bool update_sets(const struct sudoku *grid, bool possibilities[9][9][9]) {
+    bool changed = false;
+
+    for (size_t i = 0; i < 9; ++i) {
+        for (size_t j = 0; j < 9; ++j) {
+            const int val = grid->grid[i][j];
+            if (val == 0)
+                continue;
+
+            changed |= ensure_unique(possibilities, i, j, val - 1);
+            changed |= update_line(possibilities, i, j, val - 1);
+            changed |= update_column(possibilities, i, j, val - 1);
+            changed |= update_square(possibilities, i, j, val - 1);
+        }
+    }
+
+    return changed;
+}