Reconstruct the multiplication:
* * * * * * where: O C T O
* * C T O
------------- C T O B
* * * * * * T O
* * * * * * T O B E
--------------- T O B E R
O C T O B E R O B E R
B E R
B E
E R
R
are 11 prime numbers.
TOBER can only be [13613, 29173, 97673]
CTO can only be 829
CTOBER must be 829173
OCTO?: while either a 6, 7, or 9 can preceed 829 and still be prime, O has already been determined to be 9.
OCTOBER can only be one number: 9829173
its prime factors are 3 x 29 x 112979
So the multiplication can either be 112979 x 87 or 338937 x 29
However 338937 x 9 is seven digits, the graphic has six digits, so it must be:
112979
87
----------
790853
903832
----------
9829173
================
I did parts of the code in stages getting some preliminary results and using a narrowed down list for later code segments.
primes = [p for p in range(100000) if isprime(p)]
p2s = [p for p in primes if len(str(p)) == 2]
p3s = [p for p in primes if len(str(p)) == 3]
p4s = [p for p in primes if len(str(p)) == 4]
p5s = [p for p in primes if len(str(p)) == 5]
TOB = []
TOBER = []
possibleCs = []
CTO = []
OCTO = []
for p in p5s:
if p%10 not in [3,7]:
continue
if p%10000 not in p4s:
continue
if p%1000 not in p3s:
continue
if p%100 not in p2s:
continue
if (p%1000)//10 not in p2s:
continue
if p//10 not in p4s:
continue
if p//1000 not in p2s:
continue
TOB.append(p//100)
TOBER.append(p)
for t in TOB:
for c in range(1,10):
if c*1000 + t not in p4s:
continue
if c*100 + t//10 not in p3s:
continue
possibleCs.append(c)
CTO.append(c*100 + t//10)
for c in range(1,10):
if c*1000 + 829 not in p4s:
continue
OCTO.append(c*1000 + 829)
|
|
Posted by Larry
on 2024-05-03 13:56:34 |
Computer Solution
