# Rainbow cycles_the last problem.

In the explanation they use a mathematical rules to find the solution but when I compare it with mine ,the methods was different , my method isn't completely mathematic,but it gives the same result here is what I observe :

while the first number in this set is 3 so by adding 3 in each time we'll gonna a multiple of 3 . And we already know the method that let us know if a number divisible by 3 ,so if we look at 817=136 we have 1+3+6=10 and 10 are not multiple of 3 so 817 isn't orange.

Green numbers:
it started by 2:
2
2+3=5
5+3=8
8+3=11 ----> from this part if you add the numbers of the number that you get you will go back to the first 3 numbers in this set, for example here: 1+1=2 the 1st number in green set.
11+3=14 ------> 1+4=5
14+3=17 ------> 1+7=8
17+3=20 ------> 2+0=2
. . . And 817=136 -----> 1+3+6=10 and 1+0 = 1 and 1 # 2 , 5 ,8 So 136 isn't a green number.
Blue numbers:
it's the same method of the green numbers:
1
1+3=4
4+3=7
7+3=10 ------> 1+0=1
10+3=13 ------> 1+3=4
13+3=16 ------> 1+6=7
16+3=19 ------> 1+9=10 ------> 1+0=1
.
.
.
.
So 8
17=136 -------> 1+3+6=10 -------> 1+0=1
Which mean that 8*17 is a blue number.

Note by Fatima Ezzahraa
11 months, 3 weeks ago

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