Answer by user3294068 for Removing green marbles from the table
As described above, the first player loses if $N$, the initial number of marbles, is a Fibonacci number, and wins for any other integer $N > 1$. Proof follows.First, a definition.The remainder of...
View ArticleAnswer by Mike Earnest for Removing green marbles from the table
My answer offers no proof, only truth.This puzzle is related to the base Fibonacci representation of numbers. In base b, the nth digit represents $b^{n-1}$. In base Fibonacci, the nth digit represents...
View ArticleAnswer by Lacklub for Removing green marbles from the table
Let losses be on $F(x). F(1) = 3; F(2) = 5, F(x) = F(x-1) + F(x-2)$Suppose there are k marbles, and that all previous marbles N < k this Fibonacci formula decides correctly.The person to reduce the...
View ArticleAnswer by ghosts_in_the_code for Removing green marbles from the table
I'm not sure this answer works, but I think thatWe first determine a list of losing numbers. We draw a table with 2 columns and start with a number 3.Losing Previous3Now we write the greatest number...
View ArticleRemoving green marbles from the table
Alice and Bob play the following game that starts with $N\ge3$ green marbles on the table.Alice and Bob move alternatingly. Alice makes the first move. In this first move, Alice removes $x$ green...
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