Shortlisted Problems with Solutions
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For t ≤ 10 , t 6= 7, 9 , there exist infinitely many positive integers k such that repeatedly appending the digits in an alternating manner, one at a time in order from the list D
Prove that there exist two points P and Q in the plane of the triangle, one in the interior and one in the exterior of the circumcircle of ABC , such that the orthogonal projections
We also prove that a smooth positive dimensional hypersurface in projective space of even degree does not support an Ulrich bundle of odd rank and determinant of the formOXcfor some
A magic number is a positive integer with distinct digits such that the difference between the number obtained by writing its digits in descending order and the number obtained by
Size of a set Definition If there are exactlyn distinct elements in a set S, wheren is a non-negative integer, then we say S is finite and cardinality ofS is n.. A set that is not
In the adjacent figure, can the num- bers 1,2,3,4,· · ·,18 be placed, one on each line segment, such that the sum of the numbers on the three line segments meeting at each point is
The smaller of these two squares is obtained by subtractingkfrom nand the larger one is obtained by addinglto n.. Prove thatn−klis a perfect
Prove the following statements: a IfPis the incentre or an excentre ofABC, thenP is the circumcentre ofA1B1C1; b IfP is the circumcentre ofABC, thenP is the orthocentre of A1B1C1; c
