Have You Lost Your Marbles?

Probability Level 2

In Math class, you and the school bully get into a fight. Of course its the other boy's fault :-) The Math professor calls you both to his chambers, listens to your arguments and says,

"Boys, on the table you can see 11 marbles. The two of you are going to take turns removing the marbles from the table. On your turn, you can choose to take either one, two or three marbles. Whoever ends up taking the last marble from the table will go into detention."

Since you are the Math Professors favorite student, he slyly winks at you and gives you the chance to go first.

How many marbles should you pick up from the table in your first chance to avoid detention and justify the faith your Math prof has in you?

2 It does not matter 1 3

1 solution

Tanumay Datta
Mar 12, 2014

If I take 2 there remain 9 marbles. irrespestive of how many marbles he picks (lets say x) I will pick 4-x marbles. Hence after 2 such rounds only 1 marble will be left which he has to pick, and thus he loses.

Give your opponent 9 and 5 (and hence 1). When the opponent is at 9, top up a sum of 4 to be taken after being taken for 1, 2 or 3; when the opponent is at 5, top up a sum of 4 to be taken after being taken for 1, 2 or 3 again. The remained 1 must be the turn for the opponent. Taking the 1st move starting from 11 shall win the game; but if not 2 being taken, then the right to win shall be transferred to the opponent when the opponent knows how to win the game.

Answer: $\boxed{2}$

Lu Chee Ket - 5 years, 4 months ago

There are a total of 11 marbles...the headmaster instructs that the last marble whoever picks is going to be the sufferer......So in order to be a clever boy in the first turn.....I will try to pick as many marbles so that those left are odd numbers..so 2 is the call after which 9 will be left.....the moment he makes it even I will again make it odd so that he loses :)

Tanmoy Dutta - 4 years, 7 months ago

Have You Lost Your Marbles?

1 solution

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