1.If both 11

^{2} and 3

^{3} are factors of the number a * 4

^{3} * 6

^{2} * 13

^{11}, then what is the smallest possible value of a?

2.How many different positive integers exist between 10

^{6} and 10

^{7}, the sum of whose digits is equal to 2?

3.A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?

4.How many keystrokes are needed to type numbers from 1 to 1000?

5.How many integral divisors does the number 120 have?

Regards,

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