1.) A1 says that B3 is white.
2.) According to A1, B4 and B5 cannot both be the same color. According to B3, A4 is adjacent to three blacks. Since it can’t be both B4 and B5, you know that both A3 and A5 are black.
3.) B3 says that it is adjacent to three whites. A3 tells you that B2, C3, and B4 are not white. A5 tells you that one of A2 or A4 has to be grey, so only one of them can be white. Therefore both C2 and C4 are white.
4.) D1 is adjacent to four boxes. A1 tells you that D2 and E2 cannot be the same color. Therefore, according to C2, one of them is grey, and C1 and E1 are both also grey.
5.) D2 is not black according to C1. Nor is D2 white, according to A3. Therefore D2 is grey.
6.) According to B3, B4 or B5 is black. D2 tells you that it is B4.
7.) According to B4, neither B2 nor D4 is grey. Neither of them is white either, according to A3. Therefore B2 and D4 are black.
8.) According to A5 and D2, the only box that can be black in row 1 is D1.
9.) According to A1, E2 is white.
10.) E2 tells you that E3 is not white. D1 tells you that E3 is not black. Therefore E3 is grey.
11.) E3 tells you that D3 is not grey. According to D2, it’s not black either. Therefore D3 is white.
12.) D3 tells you that A4 cannot be grey. Therefore, according to A1, it must be white.
13.) According to A1, B5 must be grey.
14.) According to D4, B1 is white and A2 is grey.
14.) According to D4, D5 is white and E4 is grey.
15.) According to A5, E5 is black.
16.) You can do this step much earlier, but now you know that Column C must be the symmetric one, according to C4. This means that C5 is grey.
17.) According to A5, C3 is black.