Compute 2018 #2

Computer Science Level 2

Find the highest $9$ -digit number $\overline{abcdefghi}$ with distinct non-zero digits $a, b, c, d, e, f, g, h,$ and $i,$ such that $\overline{ab} * \overline{cd} + \overline{ef} * \overline{gh} + i = 2018.$ Note: The asterisk sign means multiplying the two $2$ -digit numbers.

The answer is 581647239.

1 solution

Zeeshan Ali
May 16, 2018

import itertools # https://docs.python.org/2/library/itertools.html#itertools.permutations
import numpy as np # http://www.numpy.org/

# set of all the possible 9 non-zero-digit numbers in decending order
permutations = list(itertools.permutations([i for i in range(9, 0, -1)], 9))

# for every p = (a, b, c, d, e, f, g, h, i) in above set
for p in permutations:
    # if all elements in p are unique
    if len(np.unique(p)) == 9:
        # if ab*cd+ef*gh+i equals 2018
        if (p[0]*10+p[1])*(p[2]*10+p[3])+(p[4]*10+p[5])*(p[6]*10+p[7])+p[8] == 2018:
            # print the elements or digits of that number 'p'
            print (p)
            # since the p's in permutations are in decending order therefore the first one satisfying
            # the condition is the larget such number, hence break (i.e. stop further search)
            break

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

Compute 2018 #2

The answer is 581647239.

1 solution

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