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Ovidiu U
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# Crossword Builder — Usage
Generate a maths crossword PDF from a list of number words.
## Basic Usage
```bash
python3 crossword_builder.py EIGHT THREE NINE SEVEN TEN FOUR
```
## Options
| Flag | Description | Default |
|------|-------------|---------|
| `--output <file>` | Output PDF filename | `crossword.pdf` |
| `--clues "WORD:eq,..."` | Custom equations per word | Auto-generated |
| `--seed <int>` | Random seed for reproducible layouts | None |
Pass a single integer to pick that many random number words:
```bash
python3 crossword_builder.py 6
```
## Examples
```bash
# Basic
python3 crossword_builder.py EIGHT THREE NINE SEVEN
# Custom output file
python3 crossword_builder.py --output my_puzzle.pdf EIGHT THREE NINE SEVEN
# Custom clues
python3 crossword_builder.py --clues "EIGHT:4+4,THREE:9-6" EIGHT THREE NINE
# Reproducible layout
python3 crossword_builder.py --seed 42 EIGHT THREE NINE SEVEN
# Combined
python3 crossword_builder.py --output my_puzzle.pdf --seed 42 EIGHT THREE NINE SEVEN
```

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"""
Maths Crossword Generator
=========================
Usage:
python3 crossword_builder.py EIGHT THREE NINE SEVEN TEN FOUR
python3 crossword_builder.py --clues "EIGHT:4+4,THREE:9-6,..." NINE SEVEN TEN FOUR
python3 crossword_builder.py --output my_puzzle.pdf EIGHT THREE NINE SEVEN TEN FOUR
The script will:
1. Find a valid crossword layout for the given words
2. Generate a printable PDF
"""
import sys
import random
import argparse
from copy import deepcopy
# ============================================================
# STEP 1: CROSSWORD SOLVER
# ============================================================
def find_intersections(w1, w2):
"""Return list of (i, j, char) where w1[i] == w2[j]."""
return [(i, j, c) for i, c in enumerate(w1) for j, c2 in enumerate(w2) if c == c2]
def build_grid(placements):
"""Build a dict {(row,col): char} from placements."""
grid = {}
for word, is_across, r, c in placements:
for i, ch in enumerate(word):
pos = (r, c + i) if is_across else (r + i, c)
grid[pos] = ch
return grid
def conflicts(placements, word, is_across, r, c):
"""Return True if placing word here conflicts with existing placements."""
grid = build_grid(placements)
word_len = len(word)
# Cell immediately before start must be empty
before = (r, c - 1) if is_across else (r - 1, c)
if before in grid:
return True
# Cell immediately after end must be empty
after = (r, c + word_len) if is_across else (r + word_len, c)
if after in grid:
return True
# Track which direction(s) occupy each cell
cell_dirs = {}
for ew, eia, er, ec in placements:
d = 'across' if eia else 'down'
for k in range(len(ew)):
pos = (er, ec + k) if eia else (er + k, ec)
cell_dirs.setdefault(pos, set()).add(d)
new_dir = 'across' if is_across else 'down'
for i, ch in enumerate(word):
pos = (r, c + i) if is_across else (r + i, c)
if pos in grid:
if grid[pos] != ch:
return True # character mismatch
if new_dir in cell_dirs.get(pos, set()):
return True # same-direction word already here
else:
# Empty cell: perpendicular neighbors must also be empty
if is_across:
n1, n2 = (r - 1, c + i), (r + 1, c + i)
else:
n1, n2 = (r + i, c - 1), (r + i, c + 1)
if n1 in grid or n2 in grid:
return True
return False
def is_connected(placements):
"""Check that all placed words form a single connected component (BFS)."""
if len(placements) <= 1:
return True
n = len(placements)
adj = [set() for _ in range(n)]
for i in range(n):
w1, ia1, r1, c1 = placements[i]
pos1 = {(r1, c1+k) if ia1 else (r1+k, c1) for k in range(len(w1))}
for j in range(i + 1, n):
w2, ia2, r2, c2 = placements[j]
pos2 = {(r2, c2+k) if ia2 else (r2+k, c2) for k in range(len(w2))}
if pos1 & pos2:
adj[i].add(j)
adj[j].add(i)
visited = {0}
queue = [0]
while queue:
curr = queue.pop()
for nb in adj[curr]:
if nb not in visited:
visited.add(nb)
queue.append(nb)
return len(visited) == n
def count_intersections(placements):
"""Count total number of cell-sharing intersections between words."""
total = 0
for i, (w1, ia1, r1, c1) in enumerate(placements):
pos1 = {(r1, c1 + k) if ia1 else (r1 + k, c1) for k in range(len(w1))}
for w2, ia2, r2, c2 in placements[i+1:]:
pos2 = {(r2, c2 + k) if ia2 else (r2 + k, c2) for k in range(len(w2))}
total += len(pos1 & pos2)
return total
def grid_bounds(placements):
"""Return (min_r, min_c, max_r, max_c) of all placements."""
cells = []
for word, is_across, r, c in placements:
for i in range(len(word)):
cells.append((r, c + i) if is_across else (r + i, c))
rows = [p[0] for p in cells]
cols = [p[1] for p in cells]
return min(rows), min(cols), max(rows), max(cols)
def normalize(placements):
"""Shift placements so grid starts at (0,0)."""
if not placements:
return placements
min_r, min_c, _, _ = grid_bounds(placements)
return [(w, ia, r - min_r, c - min_c) for w, ia, r, c in placements]
def solve(words, max_attempts=5000):
"""
Try to find a valid crossword layout for the given words.
Returns list of (word, is_across, row, col) or None.
"""
words = [w.upper() for w in words]
best = None
best_score = (-1, -1) # (words_placed, intersections)
for attempt in range(max_attempts):
random.shuffle(words)
placements = []
# Place first word horizontally at origin
first = words[0]
placements.append((first, True, 0, 0))
for word in words[1:]:
placed = False
# Try to intersect with each already-placed word
candidates = []
for existing_word, is_across, er, ec in placements:
for ei, ej, ch in find_intersections(existing_word, word):
# existing_word[ei] == word[ej] == ch
# Place new word perpendicular to existing
new_across = not is_across
if is_across:
# existing is horizontal, new word is vertical
# existing cell at (er, ec+ei), new word col = ec+ei, row = er - ej
nr, nc = er - ej, ec + ei
else:
# existing is vertical, new word is horizontal
# existing cell at (er+ei, ec), new word row = er+ei, col = ec - ej
nr, nc = er + ei, ec - ej
if not conflicts(placements, word, new_across, nr, nc):
candidates.append((word, new_across, nr, nc))
if candidates:
choice = random.choice(candidates)
placements.append(choice)
placed = True
if not placed:
# Try placing with adjacency search (wider search)
break
placements = normalize(placements)
score = (len(placements), count_intersections(placements))
if score > best_score:
best_score = score
best = placements
# Perfect solution: all words placed and connected
if len(placements) == len(words) and is_connected(placements):
return normalize(placements)
return best
# ============================================================
# STEP 2: PDF GENERATOR
# ============================================================
def generate_pdf(placements, clues_map, output_path):
try:
from reportlab.lib.pagesizes import A4
from reportlab.lib import colors
from reportlab.pdfgen import canvas as rl_canvas
from reportlab.lib.units import cm
except ImportError:
print("ERROR: reportlab not installed. Run: pip install reportlab")
sys.exit(1)
DARK_BLUE = colors.Color(0.18, 0.18, 0.55)
RED = colors.Color(0.85, 0.07, 0.07)
placements = normalize(placements)
min_r, min_c, max_r, max_c = grid_bounds(placements)
rows = max_r + 1
cols = max_c + 1
# Build letter grid
grid = [[None]*cols for _ in range(rows)]
for word, is_across, r, c in placements:
for i, ch in enumerate(word):
if is_across:
grid[r][c+i] = ch
else:
grid[r+i][c] = ch
# Number clue starts
starts = {}
for word, is_across, r, c in placements:
starts.setdefault((r, c), [])
clue_nums = {}
n = 1
for r in range(rows):
for c in range(cols):
if (r, c) in starts:
clue_nums[(r, c)] = str(n)
n += 1
# Sort words into across/down with their numbers
across_words = sorted([(w, r, c) for w, ia, r, c in placements if ia], key=lambda x: (x[1], x[2]))
down_words = sorted([(w, r, c) for w, ia, r, c in placements if not ia], key=lambda x: (x[1], x[2]))
page_w, page_h = A4
margin = 2.2 * cm
cv = rl_canvas.Canvas(output_path, pagesize=A4)
# Border
cv.setStrokeColor(DARK_BLUE)
cv.setLineWidth(3)
cv.rect(1.2*cm, 1.2*cm, page_w - 2.4*cm, page_h - 2.4*cm, fill=0, stroke=1)
# Title
cv.setFont("Helvetica-Bold", 28)
cv.setFillColor(RED)
cv.drawString(margin, page_h - 2.8*cm, "Crossword")
# Subtitle
cv.setFont("Helvetica-Bold", 14)
cv.setFillColor(DARK_BLUE)
cv.drawString(margin, page_h - 4.2*cm, "Write the answers to this puzzle in words:")
cv.drawString(margin, page_h - 5.0*cm, "ONE, TWO, THREE, ...")
# Grid sizing
max_grid_w = page_w - 2 * margin - 1*cm
max_grid_h = page_h * 0.42
cell_size = min(int(max_grid_w / cols), int(max_grid_h / rows), 38)
grid_w = cols * cell_size
grid_x = (page_w - grid_w) / 2
grid_top_y = page_h - 6.0*cm
# Draw grid
for r in range(rows):
for col in range(cols):
cx = grid_x + col * cell_size
cy = grid_top_y - r * cell_size
if grid[r][col] is not None:
cv.setFillColor(colors.white)
cv.setStrokeColor(DARK_BLUE)
cv.setLineWidth(1.2)
cv.rect(cx, cy - cell_size, cell_size, cell_size, fill=1, stroke=1)
if (r, col) in clue_nums:
cv.setFillColor(DARK_BLUE)
cv.setFont("Helvetica-Bold", 10)
cv.drawString(cx + 2, cy - 11, clue_nums[(r, col)])
# Outer grid border
cv.setStrokeColor(DARK_BLUE)
cv.setLineWidth(2.5)
cv.rect(grid_x, grid_top_y - rows * cell_size, grid_w, rows * cell_size, fill=0, stroke=1)
grid_bottom_y = grid_top_y - rows * cell_size
# Clues
clue_y = grid_bottom_y - 0.7*cm
col1_x = margin
col2_x = page_w / 2 + 0.3*cm
cv.setFont("Helvetica-Bold", 15)
cv.setFillColor(DARK_BLUE)
cv.drawString(col1_x, clue_y, "Across")
cv.drawString(col2_x, clue_y, "Down")
clue_y -= 0.55*cm
line_h = 0.62*cm
for i, (w, r, c) in enumerate(across_words):
num = clue_nums.get((r, c), "?")
eq = clues_map.get(w, "_ + _ = ?")
y = clue_y - i * line_h
cv.setFont("Helvetica-Bold", 13); cv.setFillColor(RED)
cv.drawString(col1_x, y, f"{num}.")
cv.setFillColor(DARK_BLUE)
cv.drawString(col1_x + 0.9*cm, y, eq)
for i, (w, r, c) in enumerate(down_words):
num = clue_nums.get((r, c), "?")
eq = clues_map.get(w, "_ + _ = ?")
y = clue_y - i * line_h
cv.setFont("Helvetica-Bold", 13); cv.setFillColor(RED)
cv.drawString(col2_x, y, f"{num}.")
cv.setFillColor(DARK_BLUE)
cv.drawString(col2_x + 0.9*cm, y, eq)
cv.save()
print(f"PDF saved: {output_path}")
# ============================================================
# STEP 3: MAIN
# ============================================================
NUMBER_WORDS = {
'ONE': 1, 'TWO': 2, 'THREE': 3, 'FOUR': 4, 'FIVE': 5,
'SIX': 6, 'SEVEN': 7, 'EIGHT': 8, 'NINE': 9, 'TEN': 10,
}
def generate_equation(word):
"""Generate a +/- equation with 2 or 3 operations for a number word (for ages ~6)."""
n = NUMBER_WORDS.get(word.upper())
if n is None:
return "_ + _ = ?"
num_ops = random.choice([2, 3])
for _ in range(500):
# Build operators ensuring at least one + and one -
ops = [random.choice(['+', '-']) for _ in range(num_ops)]
if len(set(ops)) < 2:
ops[random.randrange(num_ops)] = '-' if ops[0] == '+' else '+'
# Pick first num_ops numbers randomly (1–9), derive the last
nums = [random.randint(1, 9) for _ in range(num_ops)]
total = nums[0]
valid = True
for k in range(1, num_ops):
total = total + nums[k] if ops[k - 1] == '+' else total - nums[k]
if total < 0:
valid = False
break
if not valid:
continue
# Last number must satisfy: total OP last = n
last = (n - total) if ops[-1] == '+' else (total - n)
if 1 <= last <= 9:
nums.append(last)
parts = [str(nums[0])]
for op, num in zip(ops, nums[1:]):
parts.append(f"{op} {num}")
return " ".join(parts) + " = ?"
# Fallback to simple addition
for a in range(1, 10):
b = n - a
if 1 <= b <= 9:
return f"{a} + {b} = ?"
return f"= {n}"
def parse_clues(clues_str):
"""Parse 'EIGHT:4+4,THREE:9-6' into {'EIGHT': '4+4', 'THREE': '9-6'}"""
result = {}
for part in clues_str.split(","):
if ":" in part:
word, eq = part.split(":", 1)
result[word.strip().upper()] = eq.strip()
return result
def main():
parser = argparse.ArgumentParser(description="Generate a maths crossword PDF from a list of words.")
parser.add_argument("words", nargs="+", help="Words to place in the crossword (e.g. EIGHT THREE NINE)")
parser.add_argument("--clues", default="", help="Equations per word: 'EIGHT:4+4,THREE:9-6,...'")
parser.add_argument("--output", default="crossword.pdf", help="Output PDF filename")
parser.add_argument("--seed", type=int, default=None, help="Random seed for reproducible layouts")
args = parser.parse_args()
if args.seed is not None:
random.seed(args.seed)
# If a single integer is given, pick that many random number words
if len(args.words) == 1 and args.words[0].isdigit():
count = int(args.words[0])
all_words = list(NUMBER_WORDS.keys())
if count > len(all_words):
print(f"ERROR: Only {len(all_words)} number words available (ONE–TEN).")
sys.exit(1)
words = random.sample(all_words, count)
else:
words = [w.upper() for w in args.words]
clues_map = parse_clues(args.clues)
# Fill in auto-generated clues for any word without one
for w in words:
if w not in clues_map:
clues_map[w] = generate_equation(w)
print(f"Solving layout for: {', '.join(words)}")
placements = solve(words)
if not placements:
print("ERROR: Could not find a valid layout. Try different words or fewer words.")
sys.exit(1)
placed_words = [w for w, _, _, _ in placements]
missing = [w for w in words if w not in placed_words]
if missing:
print(f"WARNING: Could not place: {', '.join(missing)}")
print(f"Placed {len(placements)}/{len(words)} words")
print(f"Layout:")
for word, is_across, r, c in sorted(placements, key=lambda x: (x[2], x[3])):
direction = "across" if is_across else "down"
print(f" {word:12} {direction:6} row={r}, col={c}")
generate_pdf(placements, clues_map, args.output)
if __name__ == "__main__":
main()

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