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- Question 1 of 14
1. Question
How many ways can gold, silver and bronze be awarded to the eight finalists in a dog show?
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2. Question
How many arrangements of the letters in the word PRACTICE are possible?
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3. Question
Each project in Ms. Rose’s class is completed with a partner. Last year, each of her 26 students completed a project with every one of the other students exactly once, and Ms. Rose graded them all. How many projects did Ms. Rose grade last year?
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4. Question
A mouse is placed as shown in the maze below. If the mouse only moves up or right, how many different paths can the mouse use take to get to the cheese at the end of the maze?
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5. Question
Find the number of arrangements of the letters of the word MISSISSIPPI.
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6. Question
Seven students run a race, including Thomas and Raj. How many ways can the seven students finish first through seventh if Raj finishes ahead of Thomas (but not necessarily immediately ahead of Thomas).
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7. Question
How many distinct scalene triangles can be formed by connecting three vertices of a regular nonagon?
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8. Question
A standard checkerboard has 64 squares alternating black and red on an 8 by 8 grid. How many of the 1,296 rectangles on a checkerboard contain more than one red square?
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9. Question
How many three-digit whole numbers use only odd digits with no digit repeating?
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10. Question
Homerooms are participating in a 3-on-3 basketball tournament. How many different three-person teams can a homeroom of 15 students select to participate in the tournament?
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11. Question
Eight 4-inch square posts are placed with three feet of space between them and connected by fencing attached to the outside of the posts to form a small square enclosure. What is the perimeter of the enclosure?
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12. Question
Zip codes in the United states are five-digits long followed by a four-digit code, for example: 275138046. In North Carolina, every zip code begins with either 27 or 28. How many 9-digit zip codes are possible in North Carolina in which each digit is only used once?
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13. Question
Three identical dominoes are placed on the 3 x 4 tiled board below to create a complete pathway from the upper-left corner to the lower-right corner of the board (no dominoes may touch only at the corners). How many ways can this be done?
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14. Question
Lattice points in the form (x, y) are chosen such that:
How many ways can three of these lattice points be connected to form a triangle?
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