9 positive digits

Number Theory Level pending

The a , b , c , d , e , f , g , h , i a, b, c, d, e, f, g, h, i is a permutation of the positive digits ( 1 , 2 , , 9 1, 2, \dots, 9 ). How many different solutions does the equation below have? a b c : d e f : g h i = 1 : 2 : 3 \overline{abc}:\overline{def}:\overline{ghi}=1:2:3


The answer is 4.

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1 solution

It is not a complete solution, but the puzzle's four solutions are:

1. 192 : 384 : 576 192:384:576

2. 219 : 438 : 657 219:438:657

3. 273 : 546 : 819 273:546:819

4. 327 : 654 : 981 327:654:981

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