Other possible answers [not mentioned as an option]

Answer 1:

My reasoning:

Treat them as base 3 numbers. Like: striped = 1, white = 2, black = 0. Now, from left to right and top to bottom, we have, $$120, 010, 212$$ $$101, 202, 111$$ $$222, 121, ?$$ Translating them to decimal, we have: $$15, 3, 23$$$$10, 20 13$$ $$26,16,?$$ Now sum of the two smaller number + 1 = largest number in any column. i.e. $$15+10+1 = 26$$$$16+3+1=20$$ So the next number must be either $37$ or $10$ but $37$ will have $4$ blocks which is not the answer. So, the answer is $10$ whose base $3$ representation is $101$ and hence [striped, black, striped]

Answer 2:

Consider the decimal numbers of decoding base 3 numbers. Finding their digit sum, we get $$6,3,5$$$$1,2,4$$$$8,7,?$$. Sum of each row is a multiple of $7$. Hence, the possible answer is 6 (others are not possible since it would take a lot of digits shooting above the 3 block mark). So, possibility 1: $$6 = 0+6 = 020_3$$ Thus, black, white, black. Possibility 2: $$6 = 1+5 = 110$$[striped, striped, black]. Possibility 3: $$6=2+4 = 220$$ i.e. white, white, black.

Other possible answers [not mentioned as an option]

Answer 1:

My reasoning:

Treat them as base 3 numbers. Like: striped = 1, white = 2, black = 0. Now, from left to right and top to bottom, we have, $$120, 010, 212$$ $$101, 202, 111$$ $$222, 121, ?$$ Translating them to decimal, we have: $$15, 3, 23$$ $$10, 20, 13$$$$26,16,?$$ Now sum of the two smaller number + 1 = largest number in any column. i.e. $$15+10+1 = 26$$$$16+3+1=20$$ So the next number must be either $37$ or $10$ but $37$ will have $4$ blocks which is not the answer. So, the answer is $10$ whose base $3$ representation is $101$ and hence [striped, black, striped]

Answer 2:

Consider the decimal numbers of decoding base 3 numbers. Finding their digit sum, we get $$6,3,5$$$$1,2,4$$$$8,7,?$$. Sum of each row is a multiple of $7$. Hence, the possible answer is 6 (others are not possible since it would take a lot of digits shooting above the 3 block mark). So, possibility 1: $$6 = 0+6 = 020_3$$ Thus, black, white, black. Possibility 2: $$6 = 1+5 = 110$$[striped, striped, black]. Possibility 3: $$6=2+4 = 220$$ i.e. white, white, black.