diff --git a/Makefile b/Makefile
index ecb8727..b004aaf 100644
--- a/Makefile
+++ b/Makefile
@@ -17,7 +17,7 @@
 CFLAGS += -std=c11 -pedantic -Wall -Wextra
 CFLAGS += -O2 -flto
 
-SRC = main.c sud.c
+SRC = main.c sud.c solve.c
 OBJ = $(SRC:.c=.o)
 
 sudoku: $(OBJ)
@@ -26,7 +26,8 @@ sudoku: $(OBJ)
 clean:
 	rm -f sudoku $(OBJ)
 
-main.o: sud.h
+main.o: sud.h solve.h
 sud.o: sud.h
+solve.o: solve.h
 
 .PHONY: clean
diff --git a/main.c b/main.c
index 143f2bb..8816d2c 100644
--- a/main.c
+++ b/main.c
@@ -16,6 +16,7 @@
  * <https://www.gnu.org/licenses/>.
  */
 
+#include "solve.h"
 #include "sud.h"
 
 #include <stdint.h>
@@ -45,7 +46,17 @@ int main(void)
 
 	struct sudoku sud;
 	gen(&sud);
+	puts("Start:");
 	print(&sud);
+	putchar('\n');
+
+	bool res = solve(&sud);
+	if (!res) {
+		puts("Solver encountered an error\n");
+	} else {
+		puts("End:");
+		print(&sud);
+	}
 
 	return 0;
 }
diff --git a/solve.c b/solve.c
new file mode 100644
index 0000000..ed9fb61
--- /dev/null
+++ b/solve.c
@@ -0,0 +1,129 @@
+/*
+ * Copyright (C) 2022 Camden Dixie O'Brien
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU Affero General Public License as
+ * published by the Free Software Foundation, either version 3 of the
+ * License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * Affero General Public License for more details.
+ *
+ * You should have received a copy of the GNU Affero General Public
+ * License along with this program.  If not, see
+ * <https://www.gnu.org/licenses/>.
+ */
+
+#include "solve.h"
+
+#include <stdio.h>
+
+struct match {
+	unsigned row;
+	unsigned col;
+	unsigned val;
+};
+
+struct cellref {
+	unsigned row, col;
+	struct cellstate *state;
+};
+
+enum apply_res { ERROR, NO_MATCH, MATCH };
+
+typedef struct cellref cellgroup[NDIGITS];
+typedef bool (*rulefn)(cellgroup *group, struct match *match_out);
+
+static bool one_place_for_digit(cellgroup *group, struct match *match_out)
+{
+	for (unsigned val = 0; val < NDIGITS; ++val) {
+		unsigned n = 0, row = NDIGITS, col = NDIGITS;
+		for (unsigned i = 0; i < NDIGITS; ++i) {
+			if (!(*group)[i].state->det && (*group)[i].state->pvals[val]) {
+				row = (*group)[i].row;
+				col = (*group)[i].col;
+				++n;
+				if (n > 1)
+					break;
+			}
+		}
+
+		if (n == 1) {
+			match_out->row = row;
+			match_out->col = col;
+			match_out->val = val;
+			return true;
+		}
+	}
+
+	return false;
+}
+
+static const rulefn rules[] = {
+	&one_place_for_digit,
+};
+static const unsigned nrules = sizeof(rules) / sizeof(rules[0]);
+
+static enum apply_res apply_rules(struct sudoku *sud, cellgroup *group)
+{
+	struct match m;
+	bool matched = false;
+	for (unsigned i = 0; i < nrules; ++i) {
+		if (!rules[i](group, &m))
+			continue;
+		if (!update(sud, m.row, m.col, m.val))
+			return ERROR;
+		matched = true;
+	}
+	return matched ? MATCH : NO_MATCH;
+}
+
+bool solve(struct sudoku *sud)
+{
+	cellgroup group = { 0 };
+	unsigned r, c;
+	bool match;
+	enum apply_res res;
+
+	for (unsigned i = 0;; ++i) {
+		match = false;
+
+		/* Apply rules to each row. */
+		for (r = 0; r < NDIGITS; ++r) {
+			for (c = 0; c < NDIGITS; ++c) {
+				group[c].row = r;
+				group[c].col = c;
+				group[c].state = &sud->cells[r][c];
+			}
+
+			res = apply_rules(sud, &group);
+			if (res == ERROR)
+				return false;
+			else if (res == MATCH)
+				match = true;
+		}
+
+		/* Apply rules to each column. */
+		for (c = 0; c < NDIGITS; ++c) {
+			for (r = 0; r < NDIGITS; ++r) {
+				group[r].row = r;
+				group[r].col = c;
+				group[r].state = &sud->cells[r][c];
+			}
+
+			res = apply_rules(sud, &group);
+			if (res == ERROR)
+				return false;
+			else if (res == MATCH)
+				match = true;
+		}
+
+		/* TODO: Apply rules to each segment. */
+
+		/* Exit if no matches. */
+		if (!match)
+			return true;
+	}
+}
diff --git a/solve.h b/solve.h
new file mode 100644
index 0000000..1f65e7b
--- /dev/null
+++ b/solve.h
@@ -0,0 +1,30 @@
+/*
+ * Copyright (C) 2022 Camden Dixie O'Brien
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU Affero General Public License as
+ * published by the Free Software Foundation, either version 3 of the
+ * License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * Affero General Public License for more details.
+ *
+ * You should have received a copy of the GNU Affero General Public
+ * License along with this program.  If not, see
+ * <https://www.gnu.org/licenses/>.
+ */
+
+#ifndef SOLVE_H
+#define SOLVE_H
+
+#include "sud.h"
+
+/**
+ * Attempt to solve the given sudoku. Returns when no rules match for
+ * an entire pass over the puzzle.
+ */
+bool solve(struct sudoku *sud);
+
+#endif