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| For The Mathematically Inclined |
Anil Saigal
12/23/2008
FOR STUDENTS PROBLEM # 1 FOR GROWNUPS PROBLEM #2 Please send your solutions to anil@lokvani.com. ------------------------------------------------------------------------------------------------------------- Solution: Solution: Congratulations to Shailesh Goregaokar, who was the winner of the last set of puzzles.
Find a number ABCDEFGHIJ such that A is the count of how many 0's are in the number, B is the number of 1's, C is the number of 2's, and so on.
What is the smallest integer greater than 0 that can be written entirely with zeros and ones and is evenly divisible by 225?
Use Problem Solutions M-122508 as the subject line. Please include your full name in the text of the main message. Everyone with the right answer will be acknowledged in the next issue of Lokvani.
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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?
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?
4944.
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