def to_num(code, word):
result = 0
for c in word:
d = code[c]
result *= 10
result += d
if len(word) != lib.num_digits(result): # leading digits cannot be 0
return 0
return result
def rotate(n):
cnt = lib.num_digits(n)
result = [n]
for i in range(cnt-1):
d = n % 10
n = int(n /10)
n += d * 10**(cnt-1)
result.append(n)
return result
def get_candidates(n, filtr):
i = 0
result = []
while lib.num_digits(i) < 4:
i += n
d = digits(i)
if len(d) == 2:
d.insert(0,0)
if len(d) == 3 and nodups(d) and filtr(d):
result.append(d)
return result
#!/usr/bin/env python3
import lib
n=1
d=1
i=0
N=1000
count = 0
while i < N+1:
#print(i,str(n)+'/'+str(d),n/d)
if (lib.num_digits(n) >lib.num_digits(d)):
count += 1
#term' = 1 + 1/(1+term)
n+= d #1 + term
n,d=d,n #1/(1+term)
n+= d #1+1/(1+term)
i+=1
print(count)
cnt = {}
for d in lib.to_digits(n):
if d in cnt:
cnt[d] += 1
else:
cnt[d] = 1
return (0 in cnt and cnt[0] == 3) or \
(1 in cnt and cnt[1] == 3) or \
(2 in cnt and cnt[2] == 3)
for p in range(S, N, 2):
if not sieve[p]: continue
if not has_dups(p): continue
ln = lib.num_digits(p)
for i in range(ln - 1):
for j in range(i + 1, ln):
for k in range(j + 1, ln):
terms = []
d = 0
while d < 10:
t = lib.set_digit(p, i, d)
t = lib.set_digit(t, j, d)
t = lib.set_digit(t, k, d)
if sieve[t] and t >= p:
terms.append(t)
if 9 - d < F - len(terms):
break
d += 1
if len(terms) >= F:
def has_dups(n, digits=None):
if n == 0:
return True
if digits is None:
digits = {}
while n:
d = n % 10
n = int(n / 10)
if d in digits:
return True
digits[d] = 1
return False
products = {}
for i in range(1, 100): # 1-2 digits
if not has_dups(i):
if i < 10:
rng = range(1000, 100_000) # 3-5 digits
else:
rng = range(100, 1000) # 2-3 digits
for j in rng:
p = i * j
if eligible(i, j, p):
print(p, i, j)
products[p] = 1
if lib.num_digits(p) + lib.num_digits(i) + lib.num_digits(j) > 9:
break
print(sum(products.keys()))
pairs = []
mx = 0
for k in d:
val = d[k]
if len(val) > 1:
pairs.append(val)
pairs = sorted(pairs, key=lambda a: len(a[0]))
pairs.reverse()
MX = 10**9 # longest word has 9 chars
squares = defaultdict(list)
i = 1
while i**2 < MX:
sq = i**2
squares[lib.num_digits(sq)].append(sq)
i += 1
def assign(num, word):
code = {}
for c, d in zip(word, lib.to_digits(num)):
if c in code and code[c] != d:
return None
if d in code.values():
return None # d already mapped to a char
code[c] = d
return code
def to_num(code, word):
#!/usr/bin/env python3
import lib
count = 0
for pw in range(1, 100):
i = 1
ln = 0
while ln < pw + 1:
ln = lib.num_digits(i**pw)
if ln == pw:
print(i, '^', pw, i**pw)
count += 1
i += 1
print(count)