Beginner Logic Puzzle: Cartridge Colors Walkthrough

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(1/25) 
#1 tells you that #9 is cyan.

(2/25) 
#9 tells you that #13 is cyan.

(3/25) 
#1 tells you that no other corner is black. Therefore #13 tells you that #5 is yellow.

(4/25) 
#5 already shares a diagonal with two cyan cartridges: #9 and #13. Therefore #17 and #21 cannot be cyan. So according to #1, #21 is magenta and #25 is cyan.

(6/25) 
#25 tells you that #7 is magenta.

(7/25) 
#7 tells you that #2 cannot be black. Therefore #13 tells you that #2 must be yellow.

(8/25) 
#2 is adjacent to two magenta cartridges, one of them being #7. #6 is not magenta, according to #7. #3 is not magenta, according to #13. So #8 must be magenta.

(9/25) 
#3 cannot be black, according to #7, so according to #13, #3 must be yellow.

(10/25) 
#15 cannot be cyan, according to #9. Therefore, according to #3, #11 must be cyan.

(11/25) 
#11 says it is not adjacent to any black cartridge. #21 says it is adjacent to a black cartridge. Therefore #22 must be black.

(12/25) 
According to #21, #16 and #17 are cyan and yellow or vice versa. So #5 tells you that #16 is cyan and #17 is yellow.

(14/25) 
According to #16, #6 must be yellow.

#4 is either black or yellow, according to #13. So according to #6, it must be black.

(16/25) 
#10 is not black, according to #6. It is not cyan, according to #9. It is not magenta, according to #25. So #10 is yellow.

(17/25) 
#10 tells you that that column still needs a black and a magenta. So according to #7, #15 is magenta and #20 is black.

(19/25) 
Only the middle row and the bottom row have enough unknown cells to have three magenta cartridges. But #20 tells you that the bottom row has at least one additional black cartridge. So according to #15, #12 and #14 are both magenta.

(21/25) 
#12 tells you that #18 is black.

(22/25) 
#18 tells you that the bottom row needs at least one more magenta cartridge. According to #7, #23 cannot be magenta, so #24 must be magenta.

(23/25) 
#20 tells you that #23 must be black.

(24/25) 
#23 tells you that the fourth row cannot have any magenta cartridge. #19 also cannot be black, according to #7. It also cannot be yellow, according to #16, so #19 must be cyan.

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