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For The Mathematically Inclined

Anil Saigal
01/04/2011

PROBLEM # 1
The sum of five real numbers is 7; the sum of their squares is 10.  Find the minimum and maximum possible values of any one of the numbers.

PROBLEM #2
Find all 8-digit natural numbers n such that n2 ends in the same 8 digits as n.  Numbers are written in standard decimal notation, with no leading zeroes.

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Please send your solutions to mr.asaigal@gmail.com.

Use Problem Solutions M-122310 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.

Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com.

If you need clarification on any problem, please contact anil@lokvani.com.

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