I have been trying to solve this question.

After trying enough I read the tutorial but I am unable to understand it. I have attached the screen shot of the tutorial where I am facing problem below. The tutorial says that for n>1 and n is odd, there exists no solution because, b_n = (a_1 + a_2 + ... + a_n)%n = (1+2+3+....+n)%n = (n*(n+1)/2)%n = 0 and b_1 is already 0, and there can't be two zeros in the array b. Hence, no solution for n>1 and n is odd.

But, my doubt is that why can't I apply the same logic with n>1 and even, the same way I can prove that b_n = 0 and b_1 already 0. Hence, no solution for n>1 and n is even. Please correct me. Where am I understanding it wrong? I will be thankful for any help.