Just 9 digits

Number Theory Level 4

Find a nine digit positive integer, containing distinct digits from 1 to 9 such that ;

(i) Sum of any two consecutive digits is prime.

(ii) Sum of whose first 4 digits is equal to the sum of last 3 digits.

(iii) Sum of first, fourth and eighth digit is 13.

(iv) First, fourth and eighth digits are in increasing order, and one of them is 1.


The answer is 129476583.

Atishay Jain by atishay jain , 19, India

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1 solution

Fletcher Mattox
Apr 21, 2021 
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from itertools import permutations

def ok(t):
    primes = [2, 3, 5, 7, 11, 13, 17, 19]
    for i in range(len(t)-1):
        j = i+1
        if not t[i]+t[j] in primes:
            return False
    return True

def ok2(a, d, h):
    return 1 in [a,d,h] and a<d<h

for t in permutations(list(range(1,10))):
    a,b,c,d,e,f,g,h,i = t
    if ok(t) and a+b+c+d == g+h+i and a+d+h == 13 and ok2(a, d, h):
        print(''.join(list(map(str, t))))


1
 
129476583

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