from __future__ import division
from itertools import permutations
from re import findall
from string import maketrans
def solve(s):
'''Find solutions to alphametic equations.
>>> solve('SEND + MORE == MONEY')
9567 + 1085 == 10652
'''
words = findall('[A-Za-z]+', s)
chars = set(''.join(words)) # characters to be substituted
assert len(chars) <= 10 # there are only ten possible digits
firsts = set(w[0] for w in words) # first letters of each of word
chars = ''.join(firsts) + ''.join(chars - firsts)
n = len(firsts) # chars[:n] cannot be assigned zero
for perm in permutations('0123456789', len(chars)):
if '0' not in perm[:n]:
trans = maketrans(chars, ''.join(perm))
equation = s.translate(trans)
try:
if eval(equation):
print equation
except ArithmeticError:
pass
for alphametic in [
'SEND + MORE == MONEY',
'VIOLIN * 2 + VIOLA == TRIO + SONATA',
'SEND + A + TAD + MORE == MONEY',
'ZEROES + ONES == BINARY',
'DCLIZ + DLXVI == MCCXXV',
'COUPLE + COUPLE == QUARTET',
'FISH + N + CHIPS == SUPPER',
'SATURN + URANUS + NEPTUNE + PLUTO == PLANETS',
'EARTH + AIR + FIRE + WATER == NATURE',
('AN + ACCELERATING + INFERENTIAL + ENGINEERING + TALE + ' +
'ELITE + GRANT + FEE + ET + CETERA == ARTIFICIAL + INTELLIGENCE'),
'TWO * TWO == SQUARE',
'HIP * HIP == HURRAY',
'PI * R ** 2 == AREA',
'NORTH / SOUTH == EAST / WEST',
'NAUGHT ** 2 == ZERO ** 3',
'I + THINK + IT + BE + THINE == INDEED',
'DO + YOU + FEEL == LUCKY',
'NOW + WE + KNOW + THE == TRUTH',
'SORRY + TO + BE + A + PARTY == POOPER',
'SORRY + TO + BUST + YOUR == BUBBLE',
'STEEL + BELTED == RADIALS',
'ABRA + CADABRA + ABRA + CADABRA == HOUDINI',
'I + GUESS + THE + TRUTH == HURTS',
'LETS + CUT + TO + THE == CHASE',
'THATS + THE + THEORY == ANYWAY',
'1/(2*X-Y) == 1',
]:
print alphametic
solve(alphametic)
print
Diff to Previous Revision
--- revision 8 2009-01-14 23:52:42
+++ revision 9 2010-10-09 00:28:52
@@ -20,8 +20,11 @@
if '0' not in perm[:n]:
trans = maketrans(chars, ''.join(perm))
equation = s.translate(trans)
- if eval(equation):
- print equation
+ try:
+ if eval(equation):
+ print equation
+ except ArithmeticError:
+ pass
for alphametic in [
'SEND + MORE == MONEY',
@@ -50,6 +53,7 @@
'I + GUESS + THE + TRUTH == HURTS',
'LETS + CUT + TO + THE == CHASE',
'THATS + THE + THEORY == ANYWAY',
+ '1/(2*X-Y) == 1',
]:
print alphametic
solve(alphametic)
