Math Is Fun Forum

I want some puzzles in terminating decimals and probability with answer pls...

Advance thanks.:)

1) Given that f(x) is a polynomial of degree EIGHT such that
f(m) = 1/m for m = 1,2,3,4,5,...,9
Find f(10)

2) Suppose a²+ab+b²-c²-cd-d²=0, where a, b, c, d are positive integers.
Then I think a+b+c+d is a composite number. It is true? Prove it!

3) Prove that if p and p²+8 are prime then so is p³+4.

4) In how many ways can you change a $50 bill using $20 bills, $10 bills,
$5 bills, $2 bills, and $1 bills?

5) Find the equation of the circle which touches the axis of y at a distance 4
from the origin and cuts off an intercept of length 6 on the axis of x.