1.3 KiB
The solution to this problem is similar to problem-043. We iterate through all possible 10-digit combinations but abort most paths pretty early through a few rules. This leads to a pretty quick execution time an a not so big program.
I even managed to squeeze all in only half the available width so the other half has space enough for an ASCII representation of the magic 5-gon ring :D.
(You can see the result in the problem-068 (visual) file)
The main piece (excluding the act of pressing everything in such a small space) was formulating the rules. The more (an the earlier triggering) rules, the less paths we have to traverse and the faster our program gets: (I needed to index the elements of the ring, so I went clockwise from the outermost to the inner elements.
The rules are:
N_3 > N_0,N_5 > N_0,N_7 > N_0,N_9 > N_0. We wantN_0to be the smallest element to avoid getting the same solution multiple times, only rotated. (Also it is stated that we start counting from the smallest outer element)N_0 <= 5, otherwise it can't be the smallest outer elementN_1 <> 9,N_2 <> 9,N_4 <> 9,N_6 <> 9,N_8 <> 9, otherwise we won't get an 16-digit numberN_2+N_3+N_4 = N_0+N_1+N_2,N_4+N_5+N_6 = N_0+N_1+N_2,N_6+N_7+N_8 = N_0+N_1+N_2,N_8+N_9+N_1 = N_0+N_1+N_2. Our condition for the ring to be "magic"