For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
12/09/2008

FOR STUDENTS

PROBLEM # 1
Circles with centers A and B have radii 3 and 8, respectively. A common internal tangent intersect the circles at C and D, respectively. Lines AB and CD intersect at E, and AE = 5. What is CD?

FOR GROWNUPS

PROBLEM #2
Let n denote the smallest positive integer that is divisible by both 4 and 9, and whose base -10 representation consists of only 4's and 9's, with at least one of each. What are the last four digits of n?

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Problem Solutions 11/27/08

PROBLEM # 1
Define x # y = x³ - y. What is h # (h # h)?

Solution:

PROBLEM # 2
Compute:
(tan 41^o )(tan 42^o )(tan 43^o )(tan 44^o )(tan 45^o )(tan 46^o )(tan 47^o )(tan 48^o )(tan 49^o ).

Solution:
1.

Congratulations to Ravi Chilakamarri, Aseem Chandawarkar, Sitaram Chandawarkar, Manish Goregaokar, Shailesh Goregaokar, Suhas Joglekar, Narendran Sairam, Prateek Sahay and Muneeba Syed, who were winners of the last set of puzzles.

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