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February 20th, 2019, 01:16 PM   #11
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Thanks a lot for your help! Did anyone try to show why there aren't any less steps?

I read the answers on the link given by Estermont and realized that it would be hard to apply the problem in this one as the same logic wouldn't apply: "either always from A to B or from B to A" is not possible here...

I also read more on the Extended Euclidean Algorithm but it seems it is suited for 2 numbers instead of 3.
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February 20th, 2019, 02:21 PM   #12
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Here's a 9 :

(1) (0, 0, 6)
(2) (0, 10, 6)
(3) (10, 0, 6)
(4) (10, 6, 0)
(5) (10, 6, 6)
(6) (15, 6, 1)
(7) (11, 10, 1)
(8) (11, 0, 1)
(9) (1, 10, 1)
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February 20th, 2019, 02:25 PM   #13
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Anutter 9:

(1) (15, 0, 0)
(2) (5, 10, 0)
(3) (5, 0, 0)
(4) (0, 5, 0)
(5) (0, 5, 6)
(6) (6, 5, 0)
(7) (6, 5, 6),
(8) (6, 10, 1)
(9) (15, 1, 1)
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