Puzzle | (Something for the marmalade , Number Game)

Puzzle | Something for the Marmalade : A little girl I know sells oranges from door to door. One day while on her rounds she sold ½ an orange more than half her oranges to the first customer. To the second customer she sold ½ an orange more than half of the remainder and to the third and the last customer she sold ½ an orange more than half she now had, leaving her none.
Can you tell the number of oranges she originally had? Oh, by the way, she never had to cut an orange.

Solution:
In order that the little girl should have disposed of the oranges she had remaining after her second sale. She must have had at least one whole orange remaining so that she could deduct from it ‘half of her oranges plus half an orange’, for the third and the final sale. Therefore, if 1 orange represents half of the remaining after the second sale, then she must have sold two oranges in her second sale, leaving the 3 oranges after the first sale.
Lastly if three oranges only represent half the original number, plus half an orange, then she must have started with [(3×2) +1] or 7 oranges.

References : http://learningroots.in/uncategorized/puzzles-to-puzzle-you/

Puzzle | Number Game : A group of match sticks is placed on the table and then it is reduced in turn by each player by removing from the group at least 1 but not more than 4 match sticks. The player who takes the last match stick is the winner. If there is a group of 17 match sticks on the table, how would you make your first move, if it was your turn and how would you continue to play to win?

Solution:
The person who must move when there are 5 matchsticks must lose the game, because if that person removes one matchstick the other person will take the remaining 4, and if that person takes two the opponent will take the remaining 3, so on and so forth. Therefore, the person who moves then there are 10 or 15 matchsticks must lose. The only correct way to make the first move is to take away 2 matchsticks and reduce the pile to 15, then no matter what your opponent does on his move, you reduce the pile to 10, then to 15 and lastly you take the remaining matchsticks.

References : http://placementstudy.com/discuss/puzzles/famous-puzzles/74014521

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