Consider the following impartial combinatorial game. Two boxes each contain a nonzero number of chips. Two player alternate turns. A turn consists of a player choosing a box and emptying it, removing 0 or 1 chip from pile in the other box, then dividing the remaining chips so that both boxes again have a nonzero number of chips. Thus, (1,1) is the only terminal position. Required:
Show that (x, y) is a P-position if and only if x mod 3 = 1 and y mod 3 = 1.

What is the fewest number of full weeks briyana would have to work to have enough money? 8 weeks9 weeks 10 weeks11 weeks

Hiroaki wants to find 3 3/4 - 7/8 explain why he must rename 3 3/4 to do the subtraction.

Jace wrote a sentence as an equation. 56 is 14 more than a number. 14+ = 56 which statement best describes jace's work? jace is not correct. the phrase more than suggests using the symbol > and jace did not use that symbol. jace is not correct. he was correct to use addition, but the equation should be 56+ p = 14 jace is not correct. the first number in the sentence is 56, so the equation should start with 56. jace is correct. the phrase more than suggests addition, so jace showed that 14 plus a variable equals 56. o