9rahul u shud reply to ur q after posting
players1,2,3,........n are seated around a table, and
each has a single penny. Player 1 passes a penny to
player 2, who then passes two pennies to player 3.
Player 3 then passes one penny to Player 4, who passes
two pennies to Player 5, and so on, players alternately
passing one penny or two to the next player who still
has some pennies. A player who runs out of pennies
drops out of the game and leaves the table. Find an infinite
set of numbers n for which some player ends up
with all pennies.
-
UP 0 DOWN 0 0 10
10 Answers
9working backwards....
ending cases( A →B )
A B
1 n-1 ( For A to have 1 either it must start or it must ve got it frm another person which is impossible as it wud ve to be 0 then implying it already left table) so A starts is only possible ie n=2
A B
2 n-2 ( here someone must give A 1 penny or B itself gives)
ie
1 ) C gives A
C A B
1 1 n-2 here again C shud start in first place implying n=3
2) B gives A
A B
1 n-1
back 1 step A C B
1 2 n-3
back 1 step A D C B
1 1 1 n-3
which implies D has to start implying n=4
hence we can see n=1,2,3,4 alone satisfy
and THERE IS NO SUCH INFINITE SET as mentioned in the question !!!!!!
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9yes Eureka terrific sol !!!!!
i had messed a bit on backward reasoning and found the flaw in it :)
