I am a eight years old boy, I love candies, but my mom does not want me to eat any more candies because I start to have black teeth :( but I still love candies so...
Today when I was about to steal some candies from our candy box, my mom caught me! but strangely she wants to test my math skill and decided to give me a chance to get as many candies as I want if I win a game she just made up:
There are exactly 66 candies in this box, I will write all numbers from 1 to 66 to your board (1,2,3,4...,66) you will choose a number from the board and take that many candies from the box, but I will wipe that number so you will not able to take that many candies any more from the box. And also I will take candies from you to put back to the box with the left numbers written on the board as you do and wipe that number. then it is your turn etc... We will play this game until no number left on the board or no valid number of candies available to take from any of us (meaning if I have 20 candies, mom cannot try to take 21 candies from me)
If you can take the most candies from me at the end of the game, I will let you have that many candies just for today! otherwise, no candies and to your bed! Come on, tell me your first number!
Help me! I want to eat all candies,
is it possible? if not, how many can I get the most?
For the second case to end the game, I would like to clear with an example:
Let's say there are 50 candies in the candy box (mom's), and you have 16 candies: and somehow only 20,45,55 numbers are left on the board. if it is your mom's turn, she will not able to take any candies from you since the numbers on the board are bigger than the number of candies you have and the game ends there, have fun with your 16 candies :)