Page 46 - NUMINO Challenge_C1
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Basic Concepts Two Dishes of Marbles
Two Dishes of Marbles Game is played by two players using two dishes of
marbles. Each player takes away one or two marbles from one of the dishes
per turn. The player who takes the last marble wins.
Winning strategy
1. Take away marbles such that an equal number of marbles remain in each dish.
2. Take away marbles such that the number of marbles that remain in one dish
is a multiple of 3, and the other dish is empty.
Example There are three marbles in dish A and five marbles in dish B. If the
game is played according to the rules below, figure out how many
marbles should be taken on the first turn in order to always win.
Rules
1. Two players take turns to take one or two marbles from a dish.
2. The player who takes the last marble wins.
AB
Class Notes
In order to always win, you need to either have an equal number of remaining marbles in
both dishes, or make the number of remaining marbles in one dish a multiple of and
the other dish empty.
Since you can’t take all the marbles from one dish in one turn, you need to make the
number of marbles in each dish the same. Then, you should take the same number of
marbles as what your opponent took from the (same, different) dish in order to make sure
that both dishes have the same number of marbles.
Therefore, in order to take the last marble, you need to start (first, later) and take
marbles from dish . Then, the number of marbles in both dishes will be the
same, and you will win the game.
Puzzles 43
Two Dishes of Marbles Game is played by two players using two dishes of
marbles. Each player takes away one or two marbles from one of the dishes
per turn. The player who takes the last marble wins.
Winning strategy
1. Take away marbles such that an equal number of marbles remain in each dish.
2. Take away marbles such that the number of marbles that remain in one dish
is a multiple of 3, and the other dish is empty.
Example There are three marbles in dish A and five marbles in dish B. If the
game is played according to the rules below, figure out how many
marbles should be taken on the first turn in order to always win.
Rules
1. Two players take turns to take one or two marbles from a dish.
2. The player who takes the last marble wins.
AB
Class Notes
In order to always win, you need to either have an equal number of remaining marbles in
both dishes, or make the number of remaining marbles in one dish a multiple of and
the other dish empty.
Since you can’t take all the marbles from one dish in one turn, you need to make the
number of marbles in each dish the same. Then, you should take the same number of
marbles as what your opponent took from the (same, different) dish in order to make sure
that both dishes have the same number of marbles.
Therefore, in order to take the last marble, you need to start (first, later) and take
marbles from dish . Then, the number of marbles in both dishes will be the
same, and you will win the game.
Puzzles 43
