The number of pebbles lying on the floor is between 20 & 23 (both inclusive) and it is Samyukta’s turn to pick. If she picks 2 pebbles to ensure her win, how many pebbles were lying on the floor?
Explanation:
When two players play a game such that
• they pick balls alternately, • each player can pick balls from 1 to n, • last player to pick wins.
The winning strategy in such scenario is to leave 4k marbles in your turn.
If Samyukta picked 2 marbles to leave 4k marbles it means she would’ve picked from 4k + 2 marbles.
Between 20 and 23, only 22 is of the form 4k + 2.
∴ Samyukta picked from 22 marbles.
Hence, 22.
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