hi there, my name is seçkin i am from turkey i am a teacher in a collage i have two difficult question which i havent solve yet these are very important for me

1. there is a matrix(2-N) and i have N rectengle dominoe first edge 1 br other 2 br dominoes numbers arent important we play reverse side the problem is...

   how are we seetle one dominoe in the matrix how are we seetle two dominoes in the matrix how are we seetle three dominoes in the matrix how are we seetle four dominoes in the matrix how are we seetle five dominoes in the matrix.... what is the relation?
   
   

2. the second one is like nim problem

   two people playing a game(jack-joe) jack select a number divide the number two pieces(THEY MUSNT BE SAME) and give it to joe then joe select one,divide the number two pieces and give the numbers to jack then jack take the two number and select one and divide two pieces and give it to joe. this play continue like this...the player who has the last divide win the game.

   sample:(the first number is random)
   jack select=8 then divide 1 7
   joe select=7 then divide 2 5
   jack select=5 then divide 1 4
   joe select=4 then divide 1 3
   jack select=3 then divide 1 2
   jack win

   the problem is how must jack select a strategy to win the game i know the first one play true always he can win the number must be single(3-5-7...) or double(4-6-8...) if the number is fundemental can the result change? thanks for help...

1. I don't understrand problem 1.
   
   

2. Don't you mean "joe wins"? Joe can still select 2, then divide it as 1, 1 but then it is Jack who cannot divide anything.

   If my interpretation above is correct, it seems to me that the winning strategy is "Take an even (double) and split it into two odds (singles)". The opponent then has no other choice than to split an odd and give you back an even to choose; and the game goes on until you split 2 into 1, 1 and the opponent cannot do anything.