First of all, we wrote some of the triangular numbers in a sequence. Then we crossed out the numbers that weren't in the five times tables and the lowest number that remained was ten. Because we wrote the numbers in a sequence we knew that ten was a triangular number, which fits into two of the statements (multiple of 5 and triangular numbers).
To solve the next problem we knew that ten fitted into two of the statements already, as shown above, so we tried to divide it by three and found that it was not divisible. We then decided to write the next number in its triangular sequence, which was 15. 15 also fits into two statements, so we tried to divide it by 3 and it was divisible. Just to be safe, we divided it by 9, but it was not divisible. Therefore, 15 is the number that fits into 3 different statements (Multiply of 5, triangular number and multiples of 3 but not of 9).
To solve the last problem we wrote out a vast amount of triangular numbers whilst trying to see if they fit into all 4 sets of statements. As we went on, we found some numbers and tried to divide them by 3, 5 and 9. The numbers consisted of 136, 153 etc, we did this because in order for the number to follow all four sets it had to be a multiple of 5, a triangular number, even but not multiples of 4 and multiples of 3 but not 9. We carried on this process until we eventually got to the number 210. It fits into all four statements and was the lowest number that we could find. After all of this working out, we concluded that 210 was the smallest number that fit into these four statements.