Mario came to class, wiped the blackboard and wrote on it the numbers 1 to 50, each exactly once. Kaja is going to play with these numbers. Exactly 49 times repeats the following procedure: chooses any two numbers on board, she erases both of them, and then on the board writes the value of difference. So if you erased the numbers x and y, back write the number | x - y |, i.e. the absolute value of the difference. During the game, it may happen that it will be written on the board several times the same number. For example, if Kaja right from the start erase numbers 6 and 9, writes on the blackboard No. 3. At that time, therefore, will be on board two threes. If then erased two threes, she wrote it instead on the board number 0.
A) Does Kaja know to play the game so that it in the end remained on the board number 14? If so, how? If not, why?
B) Find absolutely all possible values that can be the end of the game on the board.
Of course, substantiate your claim. (Can you really make each of these values and how?
And can you really not make any other already? Why?)
A) Does Kaja know to play the game so that it in the end remained on the board number 14? If so, how? If not, why?
B) Find absolutely all possible values that can be the end of the game on the board.
Of course, substantiate your claim. (Can you really make each of these values and how?
And can you really not make any other already? Why?)