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February 20th, 2019, 01:16 PM  #11 
Newbie Joined: Feb 2019 From: Scotland Posts: 6 Thanks: 0 
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. 
February 20th, 2019, 02:21 PM  #12 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,580 Thanks: 1038 
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) 
February 20th, 2019, 02:25 PM  #13 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,580 Thanks: 1038 
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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fluid, form, number, steps 
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