Luogu P1008 - Triple hit

Computer Science Level 2

This problem has no inputs, and both mental calculation or programming are acceptable.

If 1 , 2 , ⋯ , 9 1,2,\cdots,9 were split into 3 3 disjoint groups and we use them to make three 3 3 -digit numbers x , y , z x,y,z , such that x : y : z = 1 : 2 : 3 x:y:z=1:2:3 , then find all possible triples for ( x , y , z ) (x,y,z) .

How to submit:

Find all possible triples for ( x , y , z ) (x,y,z) , and submit ∑ ( x + 2 y + 4 z ) \displaystyle \sum (x+2y+4z) .

Luogu Problem Set


The answer is 17187.

Alice Smith by Alice Smith , 20, China

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2 solutions

Sahil Goyat
Oct 28, 2020 
1
 
sum([17*x for x in range(100,1000) if len(set([i for i in str(x)+str(2*x)+str(3*x) if i!='0']))==9 and len(str(3*x))==3])

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David Vreken
Jul 20, 2020

The following Python code tests all possible groupings and outputs 17187 \boxed{17187} . 

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# Triple Hit
# Python

from itertools import permutations 

p = list(permutations(range(1, 10))) 
total = 0

for a in range(0, len(p)):
    x = p[a][0] * 100 + p[a][1] * 10 + p[a][2]
    y = p[a][3] * 100 + p[a][4] * 10 + p[a][5]
    z = p[a][6] * 100 + p[a][7] * 10 + p[a][8]
    if y == 2 * x and z == 3 * x:
        total += (x + 2 * y + 4 * z)

print(total)

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