Compute 2018 #4

Computer Science Level 2

Find the smallest 9 9 -digit number a b c d e f g h i ‾ \overline{abcdefghi} with distinct non-zero digits a , b , c , d , e , f , g , h , a, b, c, d, e, f, g, h, and i , i, such that a b c ‾ + b c d ‾ + c d e ‾ + f g ‾ + g h ‾ + h i ‾ = 2018. \overline{abc} + \overline{bcd} + \overline{cde} + \overline{fg} + \overline{gh} + \overline{hi} = 2018.


The answer is 178429563.

Rajen Kapur by Rajen Kapur , 72, India

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2 solutions

Zeeshan Ali
May 17, 2018 
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import itertools # https://docs.python.org/2/library/itertools.html#itertools.permutations

# set of all the possible 9 non-zero-digit numbers in acending order
permutations = list(itertools.permutations([i for i in range(1, 10)], 9))

for p in permutations: # for every p = (a, b, c, d, e, f, g, h, i) in above set
    if ((p[0]*100+p[1]*10+p[2]) # abc
        +(p[1]*100+p[2]*10+p[3]) # +bcd
        +(p[2]*100+p[3]*10+p[4]) # +cde
        +(p[5]*10+p[6]) # +fg
        +(p[6]*10+p[7]) # +gh
        +(p[7]*10+p[8])) == 2018: # +hi = 2018
        print (p) # print the elements or digits of that number 'p'
        break

(1, 7, 8, 4, 2, 9, 5, 6, 3)

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Giorgos K.
May 17, 2018

M a t h e m a t i c a Mathematica code

(f=FromDigits)@First@Select[Permutations@Range@9,f@#[[1;;3]]+f@#[[2;;4]]+f@#[[3;;5]]+f@#[[6;;7]]+f@#[[7;;8]]+f@#[[8;;9]]==2018&]

returns 178429563 \boxed{178429563}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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