Brainiest and lots of points two twins, mason and jason, play a game in which they have a pile of 99 marbles. they can take anywhere from 1 to 10 marbles each turn. whoever takes the last marble loses. mason starts. both play optimally. who wins, and how many turns will mason and jason take combined? need now

Mason wins after 18 total moves

Step-by-step explanation:

Mason's optimal strategy is to keep the total number of marbles at 11n+1, so he will take 10 marbles to start. For each move Jason makes, Mason will take a number of marbles that makes the sum from the two turns be 11.

After each of Mason's 9 turns, the number of remaining marbles will be ...

89, 78, 67, 56, 45, 34, 23, 12, 1

It doesn't matter how many marbles Jason takes. He will lose on his 9th turn.

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

i think it would be 42cm