Question

(c) 4
(d) 3.5
20. X and Y are playing a game. There are eleven
50 paise coins on the table and each player must
pick up at least one coin but not more than five.
The person picking up the last coin loses. X starts.
How many should he pick up at the start to ensure
a win no matter what strategy Y employs?
(b) 3
(C) 2
(d) 5
(a) 4​

Answer 1

Step-by-step explanation:

11 coins

min 1 max 5

so a= 1, d=5+1 =6

1, 7, 13, 19, ...

player 1 should pick coins in such a way that the remaining coins should be one of the no. in the above series

so here x picks 4 coins so that remaining coins is 7

trail 1: y picks 1

x 4 5

y 1 1 y loses

coins left 6 (=11-(4+1))

trail 2: y picks 2

x 4 4

y 2 1 y loses

coins left 5 (=11-(4+2))

trail 3: y picks 3

x 4 3

y 3 1 y loses

coins left 4

trail 4: y picks 4

x 4 2

y 4 1 y loses

coins left 3

trail 5:y picks 5

x 4 1

y 5 1 y loses

coins left 2

so x has to pick 4 to win