A is join into the game. UNFORTUNALY, the game is really dangerous. The game is Russian roulete, but very complex.

3 bullets are put into the 6-revolving chamber. Before put the bullets into the chamber, A is blindfold to let A don't know which chamber has the bullet. After put the bullets into the chamber, they take a shot. Luckly for A, A is survive.

After the first round, since A survives, they give A a chance. A has 3 choice:

-Choice 1: tell them spin the chamber randomly before the second shot;

-Choice 2: tell them to arange the bullets in the different position then spin the chamber randomly before the second shot ( but A has to be blindfold );

-Choice 3: tell them no spin the chamber and hope for the best.

Which choice A must choose to has the greatest chance of surviving?

See if you can translate and solve this.

..--- / --..-- / ....- / --..-- / ---.. / ..-. --- .-.. .-.. --- .-- ... / - .... . / .-. ..- .-.. . / .-.-.- / ...-- / --..-- / -.... / --..-- / ----. / ..-. --- .-.. .-.. --- .-- ... / - .... . / .-. ..- .-.. . / .-.-.- / .---- ----- / --..-- / ..... / --..-- / --... / ..-. --- .-.. .-.. --- .-- ... / - .... . / .-. ..- .-.. . / .-.-.- / .---- ----. / --..-- / ..--- / --..-- / .---- / ..-. --- .-.. .-.. --- .-- ... / - .... . / .-. ..- .-.. . .-.-.- / -... ..- - / ----. / --..-- / ..... / --..-- / ...-- / -.. --- -. .----. - / ..-. --- .-.. .-.. --- .-- ... / - .... . / .-. ..- .-.. . / .-.-.- / .-- .... .- - / .. ... / - .... . / .-. ..- .-.. . ..--..

A rectangle has its length is 8cm longer than its width. If we double the width, its new length is still 8cm longer its new width. What is the smallest possible area of that rectangle ?

Let  \(a@b@c=a\left(1+m\right)+a\left(2+m\right)+a\left(3+m\right)+...+a\left(10+m\right)+b\left(11+m\right)+b\left(12+m\right)+b\left(13+m\right)+...+b\left(20+m\right)+c\left(21+m\right)+c\left(22+m\right)+c\left(23+m\right)+...+c\left(30+m\right)\) ( m is some value ). If \(2@3@4=2295;9@4@2=2575;3@7@8=4420;\) will there be any solution for  \(a@b@c=1401?\) ( every value is a natural number ).

See if you can find the rules and come up with the solution.

e) 4 : 10 :: 23 : 276 :: 7 : 28 :: ? : 5050 :: 34 : ?

f) 0 : 1 :: 2 : 121 :: 5 : 15101051 :: 8 : ? :: ? : 172135352171

g) 0 : 1 :: 1 : 1 :: 2 : ? ( not 2 ) :: 3 : ? ( not 6 ) :: 4 : ? ( not 24 )

   - Bonus: What if we keep going?

See if you can figure out the rule and come up with the solution.

Ex: Decagon : 10 :: Heptadecagon : 17 :: Octagon : ? Ans: 8.
a) December : 12 :: November : 11 :: June : ?

b) 6724 : 82 :: ? : 123 :: 11664 : ?

c) Twelve : 6 :: Six : 3 :: Ten : ? ( not 3 ) :: Twenty : ? ( not 10 )

Harry has 30 candies; 8 candies has blueberry flavor; the rest has cranberry flavor. His mother, Larry also take care of Jenny, Tom and Sala. One day; some Harry's candies are disappear. Harry told mom: " Mom, someone is stolen my candies!" Harry also knows that other child did that.

Larry says: "You must tell who stolen how much candies."

Jenny says: " Sala stole 3 blueberry candies and 3 cranberry candies, mom!"
Tom says: " It was Jenny; she took 5 cranberry candies!"

Sala says: " Um.. I don't know. Maybe Jenny took 4 blueberry candies."

If 1 statement is true:

i) Who took the candy?

ii) What is the chance that Harry pick the blueberry candies without looking, if the begining has the number of the candies is the same after someone stole the candies? Express your answer as the fraction in the simplest form.