Here’s the RMO 2015 question paper of west bengal region, which was held on 6th december, in I.S.I. Kolkata.

- circles and with centers and respectively, are such that lies on Let be a point on and let be the midpoint of Let be another point on such that Then prove that the midpoint of lies on

**SOLUTION: Here** - Let be a quadratic polynomial where are real numbers. Suppose be an of positive integers. Prove that are integers.

**SOLUTION: Here** - Show that there are infinitely many triples of positive integers, such that

**SOLUTION: Here** - Suppose objects are placed along a circle at equal distances. In how many ways can objects be chosen from among them so that no two of the three chosen objects are adjacent nor diametrically opposite.

**SOLUTION:****Here** - Let be a triangle with circumcircle and incenter Let the internal angle bisectors of meet in respectively. Let intersect at and in Let intersect in Suppose the quadrilateral is a kite; that is, and Prove that is an equilateral triangle.

**SOLUTION:****Here** - Show that there are infinitely many positive real numbers, which are not integers, such that is an integer. (Here, is the fractional part of For example )

**SOLUTION:****Here**

In MP Region RMO, in question No. 4 above (RMO -West Bengal), 28 is given in place of 36. Is it printing error or there is a solution to it.

No. The question paper is correct.

If you see other region’s papers, you will see that in some paper, 36 is replaced by 32, 28.

Similarly, If you see other region’s papers then you will understand that the polynomial in question 2 has been repeated in other papers

They just twisted the problems a bit.

Yes Eeshan, I saw it. Thanks.