Math olympiads problems

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Answer

Let ABCD be a square, and E a point inside ABCD such as ABE is an equilateral triangle. What is the value of angle CÊD ? (in degrees)

In a box, there are blue balls and red balls, and we know that the number of red balls is double the number of blue balls. If we add 4 red balls, the number of red balls is 3 times the number of blue balls. What was the number of balls in the box before we added the new balls?

What is the value of 1+2+3+...+100 ?

Question

Answer

How many positive integers divide 68276 ? (Hint: 68276: 2²x13²x101)

James wants to color every positive integer between 1 and 10, but he cannot color two consecutive integers with the same color. If he has 4 different colors, how many coloring possibilities does he have? (you can use a calculator :)