195454

1)The circles that are not split up are the prime numbers.
2)On the top row, the circles that are split up only include the colors of the prime colors on the row (2,3,5,7), which makes the top row unique(the other rows have the colors of 2,3,5 in them)
3)The circles on the fifth(and last) column all include 5's color and a prime that is not 2.
4)In the far right column(tenth),the circle's colors only consist of prime colors from the top row.
5)The circles that have the colors of 2 and 3 are multiples of 6.
6)The circles that only have 2 and 3's colors are special because their only prime factors are 2 and 3.
7)The multiples of 11 appear in a diagonal line because both tens and units change by 1
8)The multiples of 9 appear in a diagonal line because tens change by 1
9)Numbers that will have three identical parts will be cubed numbers(y times y times y). There are 3 cubed numbers under 100(that aren't 1): 8(2x2x2) ,27(3x3x3) and 64(4x4x4)
10)No, you cannot find 4 consecutive circles where no color is repeated because you would need to have the color of 2 twice as one of the patterns of consecutive numbers are even, odd, even, odd e.c.t. As every even number is a multiple of 2, to find 4 consecutive circles where no color is repeated would be therefore impossible as you would need to repeat 2's color twice in the list.