Denny: Created page with "

 def all_solutions_at_most_once():     sols = set()     from functools import lru_cache     for la in range(1,6):         for lb in range(1,6):             for lc in [max..."

2025-08-24T08:08:24Z

Created page with "<pre> def all_solutions_at_most_once(): sols = set() from functools import lru_cache for la in range(1,6): for lb in range(1,6): for lc in [max..."

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<pre>
def all_solutions_at_most_once():
sols = set()
from functools import lru_cache
for la in range(1,6):
for lb in range(1,6):
for lc in [max(la,lb), max(la,lb)+1]:
if lc<1 or lc>5: continue
if la+lb+lc > 10: continue
@lru_cache(None)
def dfs(k, carry, used_mask, a_digits_tuple, b_digits_tuple, c_digits_tuple):
if k == lc:
if carry == 0 and len(a_digits_tuple)==la and len(b_digits_tuple)==lb and len(c_digits_tuple)==lc:
A = int(''.join(str(d) for d in reversed(a_digits_tuple)))
B = int(''.join(str(d) for d in reversed(b_digits_tuple)))
C = int(''.join(str(d) for d in reversed(c_digits_tuple)))
sols.add((A,B,C))
return 1
return 0
a_has = 1 if k<la else 0
b_has = 1 if k<lb else 0
a_iter = range(1,10) if a_has and k==la-1 else (range(10) if a_has else [-1])
b_iter = range(1,10) if b_has and k==lb-1 else (range(10) if b_has else [-1])
total = 0
for a_d in a_iter:
if a_d != -1 and ((used_mask>>a_d)&1):
continue
for b_d in b_iter:
if b_d != -1:
if ((used_mask>>b_d)&1) or b_d==a_d:
continue
s = carry + (0 if a_d==-1 else a_d) + (0 if b_d==-1 else b_d)
c_d = s % 10
c_carry = s // 10
if (used_mask>>c_d)&1 or c_d==a_d or c_d==b_d:
continue
if k==lc-1 and c_d==0:
continue
new_mask = used_mask | ((0 if a_d==-1 else (1<<a_d)) | (0 if b_d==-1 else (1<<b_d)) | (1<<c_d))
total += dfs(k+1, c_carry, new_mask, a_digits_tuple + (() if a_d==-1 else (a_d,)), b_digits_tuple + (() if b_d==-1 else (b_d,)), c_digits_tuple + (c_d,))
return total
dfs(0,0,0, tuple(), tuple(), tuple())
return sols

sols_at_most = all_solutions_at_most_once()
print(len(sols_at_most))
</pre>

Unique digits addition - ChatGPT - Revision history

Denny: Created page with "
def all_solutions_at_most_once(): sols = set() from functools import lru_cache for la in range(1,6): for lb in range(1,6): for lc in [max..."