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The thing about math problems is that some times there's no faster way to solve them other than to do the math. I think this is actually one of those instances, although the means of producing an answer by hand can actually be quite quick. You can start with a wrong answer and then tweak it until it becomes a correct one, and even generate a comprehensive list of solutions after you've got a correct one. Either way, congrats on solving!

yes! That's exactly what I did :)  Maybe I should rot47 the solution?  so I'll do that just to be safe about spoilers. How I solved it:  D:?46 E96C6 2C6 6=6G6? 3@I6D W@C2?86nnX 2?5 7@FCE66? 3@I6D E92E 2C6 3=F6n[ 2?5 :E ?665D E@ DF> FA E@ `bbbf[ x HC@E6 ``I Z `cJ l `bbbf]  p7E6C E92E[ x HC@E6 :E @FE 2D `cJ l `bbbf \ ``I  2?5 C65F465 :E E@ 2 =:?62C 6BF2E:@? J l `bbbf^`c \ ``^`cI] p7E6C E92E x =@@<65 7@C E96 7:CDE H9@=6 ?F>36C D@=FE:@? E92E H@C<65 H9:49 x E9:?< H2D H96? I l ``] p7E6C E92E[ x H2D 23=6 E@ D66 E92E 2E E92E A@:?E 6G6CJ `c >@C6 G2=F6D @7 I H@F=5 36 6?@F89 E@ 4C62E6 2 H9@=6 ?F>36C H96? 5:G:5:?8 3J `c W`c^`c l `X H9:49 :D 2=D@ E96 D2>6 2D 564C62D:?8 J 3J `` @7 :ED @H? G2=F6] qFE E9:D H2D 2== C62==J C62==J 92C5 7@C >6 E@ 7:8FC6 @FE 9@H E@ 7:?5 E9@D6 7C@> 2 =:?62C 6BF2E:@?P 

yeah but