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Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the...

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Page 1: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

Page 2: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

Page 3: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

Game 1

Page 4: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers, what is the shortest possible length of a side?

Page 5: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

P is the set of positive factors of 20 and Q is the set of positive factors of 12. If x is a member of set P and y is a member of set Q, what is the greatest possible value of x - y?

Page 6: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

In the right triangle ABC below, . What is the value of y?

€

y3

=3

x +y

Page 7: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

If n is divided by 9, the remainder is 5. What is the remainder if 3n is divided by 9?

Page 8: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

Let k # j be defined as the sum of all integers between k and j. For example, 5 # 9 = 6 + 7 + 8 = 21. What is the value of (80 # 110) - (81 # 109)?

Page 9: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

Page 10: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

Game 2

Page 11: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

A rectangular solid has two faces the same size and shape as figure I below and four faces the same size and shape as figure II below. What is the volume of the solid?

Page 12: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

What is the least number of 2's that can be multiplied together to yield a number greater than 50?

Page 13: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

In square PQRS below, QR = 1, RU = US, and PT = TS. What is the area of the shaded region?

Page 14: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

How many of the first one hundred positive integers contain the digit 9?

Page 15: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

If x2 + y2 = 2xy, then x must equal:

Page 16: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

Page 17: Game 1 A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers,

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