Magic numbers: Difference between revisions

Line 473:

def magic_numbers(base):

~~all~~ = []

hist = []

n = l = i = 0

while True:

l += 1

for digit in range(-n % l, base, l):

hist.extend((n + digit, l) for digit in range(-n % l, base, l))

all.append((n + digit, l))

i += 1

if i == len(~~all~~):

if i == len(hist):

return ~~all~~

return hist

n, l = ~~all~~[i]

n, l = hist[i]

n *= base

Line 488:

Line 487:

print("found", len(mn), "magic numbers")

print("the largest one is", mn[-1][0])

print("count by digits:")

print("count by number of digits:")

print(*(f"{l}:{sum(1 for _ in g)}" for l, g in groupby(l for _, l in mn)))

⚫

print(end="minimally pandigital in 1..9: ")

mn = tuple(str(m) for m, l in mn if 8 < l < 11)

⚫

print(*(m for m, l in mn if l == 9 == len(set(str(m)) - {"0"})))

print("minimally pandigital in 1..9:", 0)

⚫

print(end="minimally pandigital in 0..9: ")

⚫

print(*(m for m in mn if ~~len(m)~~ == 9 == len(set(m)~~.difference(~~"0"))))

⚫

print(*(m for m, l in mn if l == 10 == len(set(str(m)))))</syntaxhighlight>

⚫

print("minimally pandigital in 0..9:")

⚫

print(*(m for m in mn if ~~len(m)~~ == 10 == len(set(m))))</syntaxhighlight>

<pre>

found 20457 magic numbers

the largest one is 3608528850368400786036725

count by digits:

count by number of digits:

1:10 2:45 3:150 4:375 5:750 6:1200 7:1713 8:2227 9:2492 10:2492 11:2225 12:2041 13:1575 14:1132 15:770 16:571 17:335 18:180 19:90 20:44 21:18 22:12 23:6 24:3 25:1

minimally pandigital in 1..9: 0

minimally pandigital in 1..9: 381654729

⚫

minimally pandigital in 0..9: 3816547290

381654729

⚫

minimally pandigital in 0..9:

3816547290

</pre>