8/3/2019 Common Relay

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The Mathematical Relay Common

The Mathematical Crusade 2011

The Mathematical Society, Delhi Public School, R.K. Puram

Instructions

1. This question paper has 5 questions, just one page, each with a weightage of8 marks.

2. Answers need to be accompanied with adequate explanation or working, tobe entitled to full marks.

3. You are supposed to work on these questions on separate answer sheets. Thejuniors are supposed to leave their working on these questions along with thequestion paper, for their seniors to have access to the questions, as well asability to review their (the junior participants) answers. Any changes bythe seniors should accompany clear demarkation of the final solution to bechecked.

4. All working on these questions must be submitted by the final time limit of100 minutes after the commencement of the event.

QuestionsQ 1. A polyhedron has faces that are all either triangles or squares. No two square

faces share an edge, and no two triangular faces share an edge. What is theratio of the number of triangular faces to the number of square faces?

Q 2. What is the period of the function f(x) = cos(cos(x))?

Q 3. There are 15 stones placed in a line. In how many ways can you mark 5 ofthese stones so that there are an odd number of stones between any two ofthe stones you marked?

Q 4. Find all non-negative integers for which (n2

3n+ 1)2 +1 is a prime number.Explain how your answer covers all.

Q 5. What is the maximum number of knights can be placed on a chessboard suchthat no two can attack each other?

*End*

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