Maths problems (interesting ones)

[Denman]

hehe ok
here are the next couple
4)
I live in a village and I am a shopkeeper. I sell different things and all of them are sold in kg's ( i.e 1 kg, 12 kg etc.). I only sell my goods in complete kg's i.e only in whole numbers( 2.5 kg is out of scope). The problem is that I donot have
an electronic weighing machine and only have a traditional weighing machine. A friend of mine has told that I need only "4 different weights" to sell my goods if they are to be sold in the range of 1 to 40 kg. This is perfectly acceptable to me. Can you guess those 4 weights that I need to have so that I can weight anything between 1-40 kg? I am not allowed to use the weighing machine twice to weight a single request. i.e If someone wants to have 37 kg. of rice I will use those four wieghts (or less) to weigh 37 kg. of rice for him and not use the the weigh machine twise.
5)

Marbles

There are 8 marbles that weigh 1 ounce each, and 1 marble that weighs 1.1 ounces. The marbles are all uniform in size, appearance, and shape. You have a balance that contains 2 trays. You are only able to use the scale 2 times. How do you determine which marble is the heaviest using only the scale and marbles in 2 weighings

6) How do you six nines to equal exactlly 100(you can use addition, divistion, decimals... just no other digits.. ( Oh and you cant say that 99+ (99/99), because thats lame lol.... and you dont have to use all 9's)


7)
A smail is at the bottom of a 15 meter tree. He tries to reach the top. Each day, he manages to climb 4 meters, but during night, while he sleeps, he slips back 3 meters. How many days will he need to reach the top?

8)Mr and Mrs Smith have two children. You ring at their door, and one of their two children, a girl opens the door. What is the probability that the other child is also a girl? (Warning: medium difficulty )