以下的題目是剛剛1星期前比賽的題目，我只抽一些難做的。
1)
Suppose p, q are positive integers and 96/35 > p/q > 97/36, find the smallest possible value of q.
2)
Let n be a natural number, the area of the triangle bounded by the line nx + (n+1)y = √2 and the two coordinate axes is S(n). If K = S(1) + S(2) + S(3) + ... + S(2005), find the value of K.
3)
Given that 60^a = 3 and 60^b = 5. If R = 12^[(1-a-b)/2(1-b)], find the value of R.
4)
Given that p, q and r are distinct roots of the equation x^3 - x^2 + x - 2 = 0. If Q = p^3 + q^3 + r^3, find the value of Q.
5)
If B is an integer and B > (√2 + √3)^6, find the smallest possible value of B.
6)
Given that the perpendicular distances from the point O to three sides of a triangle ABC are all equal to 2 cm and the perimeter of triangle ABC is equal to 20 cm. If the area of triangle ABC is equal to k cm^2, find the value of k.
7)
In Figure 1, ten people are sitting in a round table with sitting numbers 1, 2, 3, ..., 10 respectively. Each of them chooses an integer A, B, C, ..., J respectively and tells the people on his left and right about his chosen number. Then each of them calculates the average number of the chosen numbers of his two neighbourhoods and announces this average number. If all the announced average numbers are the same as the corresponding sitting number, find the value of F. |
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發表於 3/2/2005 09:34 PM 
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