Atrey
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HELP 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

Respuesta :

sqdancefan

Answer:

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.

ahmedislife

Mason's best strategy is to stay the overall variety of marbles at 11n+1, thus he can take ten marbles to begin. for every move Jason makes, Mason can take variety of marbles that creates the add from the 2 turns be eleven.

After every of Mason's nine turns, the amount of remaining marbles are

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

It doesn't matter what number marbles Jason takes. He can lose on his ninth flip.

mason will win after 18 moves

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