Project P100
Mastermind
Codes of 4 colours from 6, scored black and white by counting colours: play against a secret code with the codes still possible counted after each answer, watch the computer's rule solve any code, or see how one guess is scored.
2 modules · 2 recorded sessionstext-menu UI in the terminalupdated 2026-10-15
Every screen below was recorded under CPython. When this page was built, the EML interpreter replayed each session from the same input and printed the same bytes.
About
Codes of 4 colours, each from 1 to 6, repeats allowed: 1,296 of them. You can guess the computer's code, watch the computer guess yours, or see how one guess is scored.
main.eml- the menu, playing, watching and scoringpegs.eml- every code, scoring, the codes that fit an answer, the computer's rule and the secret code
How each part works:
- A guess is answered with black (the right colour in the right place) and white (the right colour in the wrong place). Colours are counted with a dict, as in the corpus case
char-frequency-table. Each colour is in both codes as often as the smaller of its two counts. The total of those, minus black, is white. - After each answer, the codes still possible are the ones that would have given the same answer to the same guess. The program counts them and can give one as a hint. It also says when a guess could not have been the code.
- The computer's rule: guess 1122, then the first code, in order, that fits every answer so far. Over all 1,296 codes it never needs more than 8 guesses: 6,508 in all, 5.02 a code.
- The secret code comes from a seed, through a linear congruential generator.
What is checked: menu choices 1 to 4; a seed from 0 to 999999; codes of 4 colours, each from 1 to 6. An empty answer cancels. While playing, it stops the game and shows the code.
Sessions: sessions/basic.in gives: - a game (seed 7): two guesses that could not have been the code, two hints, and the code found in 4 guesses; - a game given up after two guesses (seed 42); - the computer solving 3456 and 1511 in 5 guesses, and 6543 in 7; - three scores: 1234 against 1325, 1122 against 2211, and 6666 against 6616.
sessions/bad-input.in gives: - menu choices 0 and x; the seed x, then a cancel; - the guesses 123, 12345, 1237 and abcd; then 1111 ten times, until no guesses are left; - a cancel, 777, and a random code whose seed is cancelled; - scores with 12, and two cancels.
Built on the verified corpus case char-frequency-table (counting with a dict, one character at a time).
Recorded sessions
What the screen shows while someone uses the program. Each typed line appears after its prompt, the way a terminal shows it.
bad-input
interpreter: byte-equal== Mastermind ==
Codes of 4 colours, each 1 to 6: black for right colour, right place; white for right colour, wrong place.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 0
Pick a number from 1 to 4.
1) play 2) watch the computer 3) score a guess 4) quit
choice> x
Pick a number from 1 to 4.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 1
seed (0 to 999999)> x
Type a whole number from 0 to 999999.
seed (0 to 999999)>
Cancelled.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 1
seed (0 to 999999)> 0
I have picked a code: 4 colours, each 1 to 6, repeats allowed. You have 10 guesses.
guess 1 (4 colours 1 to 6, ? for a hint)> 123
Type 4 colours, each 1 to 6, like 1234.
guess 1 (4 colours 1 to 6, ? for a hint)> 12345
Type 4 colours, each 1 to 6, like 1234.
guess 1 (4 colours 1 to 6, ? for a hint)> 1237
Type 4 colours, each 1 to 6, like 1234.
guess 1 (4 colours 1 to 6, ? for a hint)> abcd
Type 4 colours, each 1 to 6, like 1234.
guess 1 (4 colours 1 to 6, ? for a hint)> 1111
0 black, 0 white. 625 codes still fit every answer.
guess 2 (4 colours 1 to 6, ? for a hint)> 1111
0 black, 0 white. 625 codes still fit every answer. (That guess could not have been the code: it did not fit an earlier answer.)
guess 3 (4 colours 1 to 6, ? for a hint)> 1111
0 black, 0 white. 625 codes still fit every answer. (That guess could not have been the code: it did not fit an earlier answer.)
guess 4 (4 colours 1 to 6, ? for a hint)> 1111
0 black, 0 white. 625 codes still fit every answer. (That guess could not have been the code: it did not fit an earlier answer.)
guess 5 (4 colours 1 to 6, ? for a hint)> 1111
0 black, 0 white. 625 codes still fit every answer. (That guess could not have been the code: it did not fit an earlier answer.)
guess 6 (4 colours 1 to 6, ? for a hint)> 1111
0 black, 0 white. 625 codes still fit every answer. (That guess could not have been the code: it did not fit an earlier answer.)
guess 7 (4 colours 1 to 6, ? for a hint)> 1111
0 black, 0 white. 625 codes still fit every answer. (That guess could not have been the code: it did not fit an earlier answer.)
guess 8 (4 colours 1 to 6, ? for a hint)> 1111
0 black, 0 white. 625 codes still fit every answer. (That guess could not have been the code: it did not fit an earlier answer.)
guess 9 (4 colours 1 to 6, ? for a hint)> 1111
0 black, 0 white. 625 codes still fit every answer. (That guess could not have been the code: it did not fit an earlier answer.)
guess 10 (4 colours 1 to 6, ? for a hint)> 1111
0 black, 0 white. 625 codes still fit every answer. (That guess could not have been the code: it did not fit an earlier answer.)
No guesses left. The code was 3536.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 2
your code (4 colours 1 to 6), or random>
Cancelled.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 2
your code (4 colours 1 to 6), or random> 777
Type 4 colours, each 1 to 6, like 1234, or random.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 2
your code (4 colours 1 to 6), or random> random
seed (0 to 999999)>
Cancelled.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 3
guess (4 colours 1 to 6)> 12
code (4 colours 1 to 6)> 1234
Type 4 colours, each 1 to 6, like 1234.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 3
guess (4 colours 1 to 6)>
Cancelled.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 3
guess (4 colours 1 to 6)> 1234
code (4 colours 1 to 6)>
Cancelled.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 4
Bye.
What was typed (37 lines)
0
x
1
x
1
0
123
12345
1237
abcd
1111
1111
1111
1111
1111
1111
1111
1111
1111
1111
2
2
777
2
random
3
12
1234
3
3
1234
4
basic
interpreter: byte-equal== Mastermind ==
Codes of 4 colours, each 1 to 6: black for right colour, right place; white for right colour, wrong place.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 1
seed (0 to 999999)> 7
I have picked a code: 4 colours, each 1 to 6, repeats allowed. You have 10 guesses.
guess 1 (4 colours 1 to 6, ? for a hint)> 1122
1 black, 1 white. 208 codes still fit every answer.
guess 2 (4 colours 1 to 6, ? for a hint)> 3344
0 black, 0 white. 56 codes still fit every answer. (That guess could not have been the code: it did not fit an earlier answer.)
guess 3 (4 colours 1 to 6, ? for a hint)> ?
A code that fits every answer so far: 1255.
guess 3 (4 colours 1 to 6, ? for a hint)> 1311
3 black, 0 white. 2 codes still fit every answer. (That guess could not have been the code: it did not fit an earlier answer.)
guess 4 (4 colours 1 to 6, ? for a hint)> ?
A code that fits every answer so far: 1511.
guess 4 (4 colours 1 to 6, ? for a hint)> 1511
4 black: that is the code, in 4 guesses.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 1
seed (0 to 999999)> 42
I have picked a code: 4 colours, each 1 to 6, repeats allowed. You have 10 guesses.
guess 1 (4 colours 1 to 6, ? for a hint)> 1234
1 black, 2 white. 132 codes still fit every answer.
guess 2 (4 colours 1 to 6, ? for a hint)> 5566
1 black, 0 white. 36 codes still fit every answer. (That guess could not have been the code: it did not fit an earlier answer.)
guess 3 (4 colours 1 to 6, ? for a hint)>
You stopped. The code was 2436.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 2
your code (4 colours 1 to 6), or random> 3456
The rule: guess 1122, then the first code, in order, that fits every answer so far.
guess code answer codes left
1 1122 0 black, 0 white 256
2 3333 1 black, 0 white 108
3 3444 2 black, 0 white 12
4 3455 3 black, 0 white 2
5 3456 4 black, 0 white 1
Solved in 5 guesses. Over all 1,296 codes this rule never needs more than 8: 6,508 guesses in all, 5.02 a code.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 2
your code (4 colours 1 to 6), or random> random
seed (0 to 999999)> 7
The code is 1511.
The rule: guess 1122, then the first code, in order, that fits every answer so far.
guess code answer codes left
1 1122 1 black, 1 white 208
2 1233 1 black, 0 white 45
3 1411 3 black, 0 white 8
4 1414 2 black, 0 white 2
5 1511 4 black, 0 white 1
Solved in 5 guesses. Over all 1,296 codes this rule never needs more than 8: 6,508 guesses in all, 5.02 a code.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 2
your code (4 colours 1 to 6), or random> 6543
The rule: guess 1122, then the first code, in order, that fits every answer so far.
guess code answer codes left
1 1122 0 black, 0 white 256
2 3333 1 black, 0 white 108
3 3444 1 black, 1 white 24
4 5345 1 black, 2 white 6
5 5436 0 black, 4 white 2
6 6354 1 black, 3 white 1
7 6543 4 black, 0 white 1
Solved in 7 guesses. Over all 1,296 codes this rule never needs more than 8: 6,508 guesses in all, 5.02 a code.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 3
guess (4 colours 1 to 6)> 1234
code (4 colours 1 to 6)> 1325
colour in guess in code in both
1 1 1 1
2 1 1 1
3 1 1 1
4 1 0 0
5 0 1 0
Colours in both: 3. Right colour in the right place: 1 black. The rest, 3 - 1: 2 white.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 3
guess (4 colours 1 to 6)> 1122
code (4 colours 1 to 6)> 2211
colour in guess in code in both
1 2 2 2
2 2 2 2
Colours in both: 4. Right colour in the right place: 0 black. The rest, 4 - 0: 4 white.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 3
guess (4 colours 1 to 6)> 6666
code (4 colours 1 to 6)> 6616
colour in guess in code in both
1 0 1 0
6 4 3 3
Colours in both: 3. Right colour in the right place: 3 black. The rest, 3 - 3: 0 white.
1) play 2) watch the computer 3) score a guess 4) quit
choice> 4
Bye.
What was typed (30 lines)
1
7
1122
3344
?
1311
?
1511
1
42
1234
5566
2
3456
2
random
7
2
6543
3
1234
1325
3
1122
2211
3
6666
6616
4
Modules
The program as written, entry module first. Each module transpiles to its own Python file, which is what eml project run executes.
main.eml(entry)
eml# P100 Mastermind: guess the computer's code, watch the computer guess
# yours, or see how one guess is scored.
import pegs
def plain(s):
0 => i
len(s) => j
while i < j and s[i] == " ":
i + 1 => i
while j > i and s[j - 1] == " ":
j - 1 => j
return s[i:j]
def number(s, most):
if len(s) == 0 or len(s) > most:
return -1
0 => n
for c in s:
if not (c >= "0" and c <= "9"):
return -1
n * 10 + int(c) => n
return n
def lpad(s, n):
while len(s) < n:
" " + s => s
return s
def answer(r):
return str(r[0]) + " black, " + str(r[1]) + " white"
def still(n):
if n == 1:
return "1 code still fits every answer."
return str(n) + " codes still fit every answer."
def ask_seed():
while True:
plain(input("seed (0 to 999999)> ")) => a
if a == "":
return -1
number(a, 6) => n
if n >= 0:
return n
"Type a whole number from 0 to 999999." ^0
def play():
ask_seed() => seed
if seed == -1:
"Cancelled." ^0
return
pegs.secret(seed) => code
"I have picked a code: 4 colours, each 1 to 6, repeats allowed. You have 10 guesses." ^0
pegs.all_codes() => left
1 => turn
while turn <= 10:
plain(input("guess " + str(turn) + " (4 colours 1 to 6, ? for a hint)> ")) => g
if g == "":
("You stopped. The code was " + code + ".") ^0
return
if g == "?":
("A code that fits every answer so far: " + left[0] + ".") ^0
elif not pegs.valid(g):
"Type 4 colours, each 1 to 6, like 1234." ^0
else:
pegs.score(g, code) => r
False => fitted
for c in left:
if c == g:
True => fitted
pegs.fits(left, g, r) => left
if r[0] == 4:
("4 black: that is the code, in " + str(turn) + " guesses.") ^0
return
if fitted:
(answer(r) + ". " + still(len(left))) ^0
else:
(answer(r) + ". " + still(len(left)) + " (That guess could not have been the code: it did not fit an earlier answer.)") ^0
turn + 1 => turn
("No guesses left. The code was " + code + ".") ^0
def watch():
plain(input("your code (4 colours 1 to 6), or random> ")) => s
if s == "":
"Cancelled." ^0
return
if s == "random":
ask_seed() => seed
if seed == -1:
"Cancelled." ^0
return
pegs.secret(seed) => s
("The code is " + s + ".") ^0
elif not pegs.valid(s):
"Type 4 colours, each 1 to 6, like 1234, or random." ^0
return
"The rule: guess 1122, then the first code, in order, that fits every answer so far." ^0
" guess code answer codes left" ^0
pegs.solve(s) => rows
for k in [0:len(rows) - 1]:
rows[k] => row
(" " + lpad(str(k + 1), 5) + " " + row[0] + " " + answer(row[1]) + lpad(str(row[2]), 13)) ^0
("Solved in " + str(len(rows)) + " guesses. Over all 1,296 codes this rule never needs more than 8: 6,508 guesses in all, 5.02 a code.") ^0
def score_two():
plain(input("guess (4 colours 1 to 6)> ")) => g
if g == "":
"Cancelled." ^0
return
plain(input("code (4 colours 1 to 6)> ")) => c
if c == "":
"Cancelled." ^0
return
if not pegs.valid(g) or not pegs.valid(c):
"Type 4 colours, each 1 to 6, like 1234." ^0
return
pegs.counts(g) => cg
pegs.counts(c) => cc
" colour in guess in code in both" ^0
0 => both
for k in ["1", "2", "3", "4", "5", "6"]:
0 => a
0 => b
if k in cg:
cg[k] => a
if k in cc:
cc[k] => b
if a > 0 or b > 0:
a => m
if b < a:
b => m
both + m => both
(" " + lpad(k, 6) + lpad(str(a), 10) + lpad(str(b), 9) + lpad(str(m), 9)) ^0
pegs.score(g, c) => r
("Colours in both: " + str(both) + ". Right colour in the right place: " + str(r[0]) + " black. The rest, " + str(both) + " - " + str(r[0]) + ": " + str(r[1]) + " white.") ^0
"== Mastermind ==" ^0
"Codes of 4 colours, each 1 to 6: black for right colour, right place; white for right colour, wrong place." ^0
True => running
while running:
"" ^0
"1) play 2) watch the computer 3) score a guess 4) quit" ^0
plain(input("choice> ")) => choice
if choice == "1":
play()
elif choice == "2":
watch()
elif choice == "3":
score_two()
elif choice == "4":
False => running
else:
"Pick a number from 1 to 4." ^0
"Bye." ^0
Python projection (main.py)
import pegs
def plain(s):
i = 0
j = len(s)
while i < j and s[i] == " ":
i = i + 1
while j > i and s[j - 1] == " ":
j = j - 1
return s[i:j]
def number(s, most):
if len(s) == 0 or len(s) > most:
return -1
n = 0
for c in s:
if not (c >= "0" and c <= "9"):
return -1
n = n * 10 + int(c)
return n
def lpad(s, n):
while len(s) < n:
s = " " + s
return s
def answer(r):
return str(r[0]) + " black, " + str(r[1]) + " white"
def still(n):
if n == 1:
return "1 code still fits every answer."
return str(n) + " codes still fit every answer."
def ask_seed():
while True:
a = plain(input("seed (0 to 999999)> "))
if a == "":
return -1
n = number(a, 6)
if n >= 0:
return n
print("Type a whole number from 0 to 999999.")
def play():
seed = ask_seed()
if seed == -1:
print("Cancelled.")
return
code = pegs.secret(seed)
print("I have picked a code: 4 colours, each 1 to 6, repeats allowed. You have 10 guesses.")
left = pegs.all_codes()
turn = 1
while turn <= 10:
g = plain(input("guess " + str(turn) + " (4 colours 1 to 6, ? for a hint)> "))
if g == "":
print("You stopped. The code was " + code + ".")
return
if g == "?":
print("A code that fits every answer so far: " + left[0] + ".")
elif not pegs.valid(g):
print("Type 4 colours, each 1 to 6, like 1234.")
else:
r = pegs.score(g, code)
fitted = False
for c in left:
if c == g:
fitted = True
left = pegs.fits(left, g, r)
if r[0] == 4:
print("4 black: that is the code, in " + str(turn) + " guesses.")
return
if fitted:
print(answer(r) + ". " + still(len(left)))
else:
print(answer(r) + ". " + still(len(left)) + " (That guess could not have been the code: it did not fit an earlier answer.)")
turn = turn + 1
print("No guesses left. The code was " + code + ".")
def watch():
s = plain(input("your code (4 colours 1 to 6), or random> "))
if s == "":
print("Cancelled.")
return
if s == "random":
seed = ask_seed()
if seed == -1:
print("Cancelled.")
return
s = pegs.secret(seed)
print("The code is " + s + ".")
elif not pegs.valid(s):
print("Type 4 colours, each 1 to 6, like 1234, or random.")
return
print("The rule: guess 1122, then the first code, in order, that fits every answer so far.")
print(" guess code answer codes left")
rows = pegs.solve(s)
for k in range(0, len(rows)):
row = rows[k]
print(" " + lpad(str(k + 1), 5) + " " + row[0] + " " + answer(row[1]) + lpad(str(row[2]), 13))
print("Solved in " + str(len(rows)) + " guesses. Over all 1,296 codes this rule never needs more than 8: 6,508 guesses in all, 5.02 a code.")
def score_two():
g = plain(input("guess (4 colours 1 to 6)> "))
if g == "":
print("Cancelled.")
return
c = plain(input("code (4 colours 1 to 6)> "))
if c == "":
print("Cancelled.")
return
if not pegs.valid(g) or not pegs.valid(c):
print("Type 4 colours, each 1 to 6, like 1234.")
return
cg = pegs.counts(g)
cc = pegs.counts(c)
print(" colour in guess in code in both")
both = 0
for k in ["1", "2", "3", "4", "5", "6"]:
a = 0
b = 0
if k in cg:
a = cg[k]
if k in cc:
b = cc[k]
if a > 0 or b > 0:
m = a
if b < a:
m = b
both = both + m
print(" " + lpad(k, 6) + lpad(str(a), 10) + lpad(str(b), 9) + lpad(str(m), 9))
r = pegs.score(g, c)
print("Colours in both: " + str(both) + ". Right colour in the right place: " + str(r[0]) + " black. The rest, " + str(both) + " - " + str(r[0]) + ": " + str(r[1]) + " white.")
print("== Mastermind ==")
print("Codes of 4 colours, each 1 to 6: black for right colour, right place; white for right colour, wrong place.")
running = True
while running:
print("")
print("1) play 2) watch the computer 3) score a guess 4) quit")
choice = plain(input("choice> "))
if choice == "1":
play()
elif choice == "2":
watch()
elif choice == "3":
score_two()
elif choice == "4":
running = False
else:
print("Pick a number from 1 to 4.")
print("Bye.")
pegs.eml
eml# P100 Mastermind - codes of 4 colours, 1 to 6, repeats allowed: 1,296 of
# them. A guess is answered with black (right colour, right place) and
# white (right colour, wrong place), counted colour by colour with a dict
# as in the corpus case char-frequency-table. The computer's rule: guess
# 1122, then the first code, in order, that fits every answer so far.
def all_codes():
[] => out
for a in [1:6]:
for b in [1:6]:
for c in [1:6]:
for d in [1:6]:
out + [str(a) + str(b) + str(c) + str(d)] => out
return out
def valid(s):
if len(s) != 4:
return False
for c in s:
if not (c >= "1" and c <= "6"):
return False
return True
def counts(s):
{} => out
for c in s:
if c in out:
out[c] + 1 => out[c]
else:
1 => out[c]
return out
def score(guess, code):
# [black, white]: black counts the places that match; every colour
# matches as often as it is in both, the fewer of the two counts, and
# white is what that leaves beyond black.
0 => black
for i in [0:3]:
if guess[i] == code[i]:
black + 1 => black
counts(guess) => g
counts(code) => k
0 => both
for c in g:
if c in k:
if g[c] < k[c]:
both + g[c] => both
else:
both + k[c] => both
return [black, both - black]
def fits(codes, guess, answer):
# the codes that would have given this answer to this guess
[] => out
for c in codes:
score(guess, c) => r
if r[0] == answer[0] and r[1] == answer[1]:
out + [c] => out
return out
def solve(code):
# [[guess, answer, codes still fitting], ...] until 4 black
all_codes() => left
"1122" => guess
[] => out
True => going
while going:
score(guess, code) => r
fits(left, guess, r) => left
out + [[guess, r, len(left)]] => out
if r[0] == 4:
False => going
else:
left[0] => guess
return out
def secret(seed):
# 4 colours from a linear congruential generator, top 16 bits
seed => x
"" => out
for i in [1:4]:
(1664525 * x + 1013904223) % 4294967296 => x
# x is below 2 ** 32, so the division is exact
out + str(int((x - x % 65536) / 65536) % 6 + 1) => out
return out
Python projection (pegs.py)
def all_codes():
out = []
for a in range(1, 7):
for b in range(1, 7):
for c in range(1, 7):
for d in range(1, 7):
out = out + [str(a) + str(b) + str(c) + str(d)]
return out
def valid(s):
if len(s) != 4:
return False
for c in s:
if not (c >= "1" and c <= "6"):
return False
return True
def counts(s):
out = {}
for c in s:
if c in out:
out[c] = out[c] + 1
else:
out[c] = 1
return out
def score(guess, code):
black = 0
for i in range(0, 4):
if guess[i] == code[i]:
black = black + 1
g = counts(guess)
k = counts(code)
both = 0
for c in g:
if c in k:
if g[c] < k[c]:
both = both + g[c]
else:
both = both + k[c]
return [black, both - black]
def fits(codes, guess, answer):
out = []
for c in codes:
r = score(guess, c)
if r[0] == answer[0] and r[1] == answer[1]:
out = out + [c]
return out
def solve(code):
left = all_codes()
guess = "1122"
out = []
going = True
while going:
r = score(guess, code)
left = fits(left, guess, r)
out = out + [[guess, r, len(left)]]
if r[0] == 4:
going = False
else:
guess = left[0]
return out
def secret(seed):
x = seed
out = ""
for i in range(1, 5):
x = (1664525 * x + 1013904223) % 4294967296
out = out + str(int((x - x % 65536) / 65536) % 6 + 1)
return out