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.

----------------------------------------------------------------------------------------------------------

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.

-------------------------------------------------------------------------------------------------------------

Problems from 12/09/10

PROBLEM # 1
What is the area of the largest square that can be completely inscribed in a triangle whose sides 3,4 and 5 inches?

SOLUTION
(12/7)^2.

PROBLEM # 2
A rectangular sheet of paper is folded so that two diagonally opposite corners come together.  If the crease formed is the same length as the longer side of the sheet, what is the ratio of the longer side of the sheet to the shorter side?

|