How many two-digit numbers N have the property that the sum of N and the number formed by reversing the digits of N is a perfect square ?The square SAMF has an area of 169. It contains two over lapping squares. The smaller of these sqares has an area that is one quarter of the larger of them, and the erea of their overlap is 4. What is the erea of the shaded region ?In the diagram, each of the integers 1 through 9 is to be placed in one circles, both horizontal and diagonal, add to 18. The 6 and 1 have been filled in as shown. Determine the value of the number represented by x in the diagram. Justify your answerHow many digits does the number 20¹³ have ?

The Game of Squares

Either boys or girls, usually aged from seven to ten, play the two-person game of"Mandarin's Box". They draw a rectangle on the ground and (1)……….. it into ten smallsquares called "rice fields" or "fish ponds”.

They also draw two additional semi-circular boxesat the two (2)………. of the rectangle, which are called"mandarin's boxes" - the game's name. Each person has 25 small pebbles and a bigger stone.

Each player places the stone in one of the mandarin's boxes and five small pebbles in each of the other squares. Then the game begins. The first player takes up the contents of one square on his or her side ofthe board, but not a mandarin's box and distributes the pebbles one by one, (3)……….. with the next square in (4)………. direction. Since each square contains five pebbles at the beginning, the first move will distribute five pebbles to the left or right.

After the last pebble is distributed, the player takes the contents of the following squareand repeats the distribution (5)………... But if the following square is one of the mandarin's boxes, the turn ends and passes to the other player.

If the last pebble falls into a square that precedes one empty square, the player wins all the contents of the square following the empty square and (6)……….these pebbles from the board. However, if there are two or more empty squares in a row, the player (7)…….. his or her turn.

Once a player has taken pebbles from the board, the turn is (8)……….to the other player. If all five squares on one player's side of the board are emptied at any time, that player must place one pebble he or she has aside back in each of the five squares so that the game can resume.

The game (9)………until the two mandarins' boxes have both been (10)……….. At the end of the game, the player with more pebbles wins, with each of the large stones counting as ten points.

Question 1

A.share

B.divide

C.separate

D.leave