diff --git a/src/bin/generator.rs b/src/bin/generator.rs
index 83d748f..38d1a86 100644
--- a/src/bin/generator.rs
+++ b/src/bin/generator.rs
@@ -98,6 +98,7 @@ fn main() {
     let mut difficulty = Difficulty::Hard;
     let mut threads = 1;
     let mut print_possibilities = false;
+    let mut alternative_generation = false;
 
     {
         // this block limits scope of borrows by ap.refer() method
@@ -141,14 +142,25 @@ fn main() {
         );
 
         ap.refer(&mut print_possibilities).add_option(
-            &["-p", "--possibilities"],
+            &["-p", "--pencils"],
             argparse::StoreTrue,
-            "Include each cell's possibilities in the output; applies only to PDF output",
+            "Include each cell's pencil marks in the output; applies only to PDF output",
+        );
+
+        ap.refer(&mut alternative_generation).add_option(
+            &["--alt"],
+            argparse::StoreTrue,
+            "Generate using an alternative style of generation",
         );
 
         ap.parse_args_or_exit();
     }
 
+    print_possibilities = print_possibilities | alternative_generation;
+    if alternative_generation {
+        max_hints = 81*9;
+    }
+
     let max_attempts = max_attempts.unwrap_or(100 * number_puzzles);
 
     let solve_controller = difficulty.map_to_solve_controller();
@@ -168,6 +180,7 @@ fn main() {
                 &AtomicI64::new(number_puzzles as i64),
                 &AtomicI64::new(max_attempts as i64),
                 debug,
+                alternative_generation,
             )
         }
 
@@ -179,6 +192,7 @@ fn main() {
             debug,
             solve_controller,
             difficulty,
+            alternative_generation,
         ),
     };
 
@@ -230,6 +244,7 @@ fn run_multi_threaded(
     debug: bool,
     solve_controller: SolveController,
     difficulty: Difficulty,
+    alternative_generation: bool,
 ) -> Vec<GeneratedGrid> {
     let mut thread_rng = thread_rng();
     let (transmitter, receiver) = mpsc::channel();
@@ -259,6 +274,7 @@ fn run_multi_threaded(
                 &*puzzles_left,
                 &*attempts_left,
                 debug,
+                alternative_generation,
             );
 
             let num_puzzles_found = found_puzzles.len();
@@ -300,13 +316,16 @@ fn get_puzzle_matching_conditions<R: Rng>(
     puzzles_left: &AtomicI64,
     attempts_left: &AtomicI64,
     debug: bool,
+    alternative_generation: bool,
 ) -> Vec<GeneratedGrid> {
 
     let mut generated_grids: Vec<GeneratedGrid> = Vec::new();
 
     while attempts_left.fetch_sub(1, Ordering::SeqCst) > 0 && puzzles_left.load(Ordering::SeqCst) > 0 {
-        let (grid, num_hints, statistics) =
-            sudoku_solver::generator::generate_grid(rng, &solve_controller);
+        let (grid, num_hints, statistics) = match alternative_generation {
+            true => {sudoku_solver::generator::generate_alternate_grid(rng, &solve_controller)}
+            false => {sudoku_solver::generator::generate_grid(rng, &solve_controller)}
+        };
 
         if debug {
             println!("Found puzzle with {:#?}", statistics);
diff --git a/src/generator.rs b/src/generator.rs
index 2d6c18f..eec1a27 100644
--- a/src/generator.rs
+++ b/src/generator.rs
@@ -178,6 +178,92 @@ pub fn generate_grid<R: Rng>(
     (grid, num_hints, statistics_option.unwrap())
 }
 
+pub fn generate_alternate_grid<R: Rng>(
+    rng: &mut R,
+    solve_controller: &SolveController,
+) -> (Grid, u64, SolveStatistics) {
+    let mut grid = generate_completed_grid(rng);
+
+
+    let mut cell_order_vec = Vec::new();
+    // go through and replace every number with a pencil marking
+    for x in 0..9 {
+        for y in 0..9 {
+            let mut cell = grid.get(x, y).unwrap();
+            cell_order_vec.push(Rc::clone(&cell));
+
+            if let CellValue::Fixed(digit) = cell.get_value_copy() {
+                cell.set_value_exact(CellValue::Unknown(vec![digit]));
+            } else {
+                panic!("Unexpectedly found an incomplete cell in a completed puzzle");
+            }
+
+        }
+    }
+
+    // Need to randomly reorder non_empty_cells
+    cell_order_vec.shuffle(rng);
+
+    fn invert_digits(digits: &[u8]) -> Vec<u8>{
+        let mut inverted = Vec::with_capacity(9);
+
+        for i in 1..=9 {
+            if !digits.contains(&i) {
+                inverted.push(i);
+            }
+        }
+
+        inverted
+    }
+
+    let mut num_pencils = 81;
+    for cell in cell_order_vec {
+        let mut current_digits = match cell.get_value_copy() {
+            CellValue::Fixed(digit) => {vec![digit]}
+            CellValue::Unknown(digits) => {digits}
+        };
+
+        let to_try_add = invert_digits(&current_digits);
+        for digit in to_try_add {
+            current_digits.push(digit);
+            cell.set_value_exact(CellValue::Unknown(current_digits.clone()));
+
+            let (status, _) =
+                evaluate_grid_with_solve_controller(&grid, solve_controller);
+            match status {
+                SolveStatus::Complete(uniqueness) => {
+                    let uniqueness = uniqueness.unwrap();
+                    match uniqueness {
+                        Uniqueness::Unique => {
+                            num_pencils += 1;
+                        }
+                        Uniqueness::NotUnique => {
+                            // Too relaxed; can't add this pencil mark
+                            current_digits.pop();
+                        }
+                    }
+                }
+                SolveStatus::Unfinished => {
+                    panic!("evaluate_grid_with_solve_controller should never return UNFINISHED")
+                }
+                SolveStatus::Invalid => {
+                    println!("{}", grid);
+                    panic!("Removing constraints should not have set the # of solutions to zero")
+                }
+            }
+        }
+
+        cell.set_value_exact(CellValue::Unknown(current_digits));
+
+    }
+
+    let (_, statistics) =
+        evaluate_grid_with_solve_controller(&grid, solve_controller);
+
+    (grid, num_pencils, statistics)
+
+}
+
 // We generate a completed grid with no mind for difficulty; afterward generate_puzzle will take out as many fields as it can with regards to the difficulty
 fn generate_completed_grid<R: Rng>(rng: &mut R) -> Grid {
     let solve_controller = SolveController {