so to win in a Fibonacci Nim there are
certain strategies to follow the
first thing we have to know before that
is to understand the concept of the
Fibonacci sequence so what is the
Fibonacci sequence it is actually formed
from numbers with like they are formed and
that are formed with the
summation of the previous two numbers so
let's have a look at a Fibonacci
sequence so basically it is the sequence
that looks like something like this and
taking 55 for instance 55 is just the addition of
21 plus 34 which is the previous two
numbers okay so now basically to win in a Fibonacci Nim the only strategy is
to leave a Fibonacci number of the coins
at the end of the players turn so for
instance this is a pile of coins and
each player would take turn to remove some
number of coins right so a player one
would try to remove a number of coins so
that the remaining number of coins would
be just a Fibonacci numbers um so
basically how to win is to that player one
should actually just break down the
number of coins into a series with
would be Fibonacci numbers and the
numbers should be non-repeating and
non-adjacent so looking at 57 57 is
actually formed with 55 plus two and player one could not remove 55 coins because
it would just let player two win by
removing the remaining two coins so the
only step player one could do is just to
remove two coins from the pile of coins
but as you see the coins remove should
actually be the smallest number of the
Fibonacci numbers to actually minimize the
options for the opponent in this sense
player two so I had a game with the
computer online however because
the game is too long winded so I
decided to not record it but write it
down and as you could see from here we
begin with fifty seven coins so as what I
say I break down just I broke down just
out it was two and
continues like this and player one is me
and player two is the computer if you
need more time you can actually
pause and have a look so basically it's just me keep
it keep on deducing the non-Fibonacci
numbers into a series of non-adjacent
non-repeating Fibonacci
numbers and then I will just keep on
removing the smallest number and then
like when you can see in the end
there's three coins left no matter the
computer remove one or two coins
I would definitely win by removing the
remaining coins so um this is a
strategy so if the number is a non
Fibonacci number then player one
would always win with this strategy
unless they did a mistake however if the
initial number of point is a Fibonacci
number player two can win instead in an
optimal condition this is because
breaking down the Fibonacci number
will form the two previous Fibonacci
numbers so let's take 55 as the example
so breaking down it will just be
34 plus 21 because the previous like
largest Fibonacci number is just 34 and
then if I try to remove 34 or 21 it
would just let player two win by
removing the remaining number of coins
so I would try to actually remove a
smaller number of coins like for
instance if I remove 4 and then will
leave 51 coins and then player two could just
deduce it back into a series of Fibonacci coins Fibonacci numbers so like
this and remove one coin and the game
will actually continue like what we had
just now but in this sense player two
stands the chance to win because it
goes at it looks like this step but
instead of player one removing one coin in
this chance player 2 is the one who
removed one coin and the whole game
continues as the same thing just one and
two swapped and in the end player
two would actually win instead of player one
