1.Find the largeset four-digit number in which all digits are prime numbers.
2.Let (n) be a positive integer. It is known that 20090124 leaves a remainder of 4 when divided by (n). Find the smallest possible value of (n).
3.If the fraction (a/b) <where (a),(b) are positive is 1. Find the smallest possible value of (b).
4.A rectangle with integral side lengths has area 23. Find its perimeter.
5.In the figure, (ABCD) and (AEFG) are squares with side lengths 12 and 16 respectively. (EG) meets (BC) at (M) and (CD) at (N). Find the area of triangle (CMN).
6.In the figure, (IB) and (IC) are the bisectors of <B and <C of triangle (ABC) respectively. If <BIC = 140 degree and <BAC = x degree, find (x).
7.Let (n) be an integer greater that 1. If the sun of digits of (n*n) and (n*n*n) are both a while the sun of digits of (n*n*n*n) is (b), find the smallest possible value of (b).
8.What is the remainder when the 2009-digit number 1000...0001 is divided by 11?
9.In the grids shown, adjacent lines are 1 unit apart. If a maze-like figure of 120 units, how many right angles would have been drawn?
10.In the figure, (D),(E),(F) are points on (AB), (BC) and (CA) of triangle(ABC) respectively such that (BD)=(BE) and (CE)=(CF). If triangle(ADF) is equilateral and triangle(DEF) = x degree,(x).