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so i broke the problem into 2 problem i think that this might be possible.
proving that every even number is here
note: their is an algoritme (in the colour )in every column for example column a is 4/4/4/ b is 3/2/3/2/3 and every column has one
 
proving that when using the conjecture for every odd number leads to a number in the previous row i tested it for the first few number and you always get a number out of 1 row above but multiple rows above would also be good
 

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