IQ Test

來自：ywsing0
時間：Wed Jan 25 13:35:04 2006

o殊, 慢慢做.

1. pythagorean number is a set of three integers: a, b, c which staisfy following condition.
a2 + b2 = c2
write a program to list all of the pythagorean number up to 1000
(Use C,C++,C#, Java or BASIC)

2. consider a pair of two positive integers (m,n) which satisfy following two conditions
7m+3n = 102004
n/m is integer
how many pairs of such two integers exist?

3. There are n positive variables A1, A2, A3, ...An. Consider A that is the minimum value of following numbers
A1 / (1+A1), A2 / (1+A1+A2), ... An / (1+A1+A2+...+An)
What becomes of maximum value of A when each variable changes meeting the following condition?
A1 + A2 + A3 + ... + An = 1

4. There are two figures on the same plane. one is an equilateral triangle OAB whose length of one side equals 1 and the other is a line m, which passes point O but does not cross side AB. And A' and B' are cross points between line m and altitudes to m each from A and B. Calculate maximum value of AA' + BB'.