Set 1) Multiples of 5 are 5,10,15,20,25,30,35,40,45 etc.
Set 2) Triangular numbers are 1,3,6,10,15,21,28,36,45 etc.
Set 3) Multiples of 2 but not of 4 are 2,6,10,14,18,22,26 etc.
Set 4) Multiples of 3 but not of 9 are 3,6,12,15,21 etc.
1. The number 21 belongs to 2 of the sets (2 & 4)
The number 3 also belongs to the sets 2 & 4
2. The number 6 belongs to 3 of the sets (2,3 & 4)
The number 10 belongs to 3 of the sets (1,2 & 3)
The number 15 belongs to 3 of the sets (1,2 & 4)
3. The smallest number that would fit in all four sets ends in 0 as it is a multiple of 5,
and is also even. (as it is a multiple of 2 as well)
Therefore, the smallest number that would fit in all 4 sets is 210!
210 is divisible by 2,3 and 5 but not divisible by 4 and 9. ( It is also a triangular
number! )
4. The pattern of sets 1 and 3, is that the difference in the corresponding number in
that sequence increments by 1.
For example, the difference of the first 2 numbers in sets 1&3 is 5-2 = 3
The difference of the next 2 numbers in sets 1&3 is 10-6 = 4
The difference of the next 2 numbers in sets 1&3 is 15-10 = 5
And so on...
5. The pattern of sets 1 and 4, is that the difference in the corresponding
alternate number in that sequence increments by 1.
For example, the 1st, 3rd & 5th difference increase by 1 (2,3,4..) and the 2nd,
4th & 6th difference also increase by 1 (4,5,6..) :
The 1st difference is 5-3 = 2
The 3rd difference is 15-12 = 3
The 5th difference is 25-21 = 4
The 2nd difference is 10-6 = 4
The 4th difference is 20-15 = 5
The 6th difference is 30-24 = 6
And so on...