Round 1a
Round 1b
Double Time
The Triple
Risky Business
200
List all the arrangements of the letters in the word ‘T’. How many are there?
T, 1
200
List all the arrangements of the letters in the word ‘TI’. How many start with ‘T’? How many with ‘I’? How many are there?
2 arrangements
1
1
200
How many of the factorials from 1! to 100! are divisible by 9?
95
200
How many positive integers less than 500 can be written as the sum of two positive perfect cubes?
26
(construct a table with perfect cubes on top row and 1st column)
200
How many 3-letter combinations can be formed if the second letter must be a vowel (A, E, I, O, or U), and the third letter must be different from the first letter?
2x5x25 = 3,250
300
You have 5 shirts, 6 pairs of pants, and 8 hats. How many outfits can you make consisting of one shirt, one pair of pants, and one hat?
5x6x8=240
300
Mr. Stewart’s math class has 16 boys, and 22 of his students bring their calculators to class. If 13 of the students with calculators are girls, then how many boys didn’t bring their calculators to class?
7
300
What is the units digit of the sum 
3
300
What is the greatest common factor of 5!, 10!, and 15!?
5!
300
My classroom has 11 rows of chairs, with 11 chairs in each row. The chairs in each row are numbered from 1 to 11.
11 x 6 = 66
400
The local theater has one ticket window. In how many ways can six people line up to buy a ticket?
6! = 720
400
How many 3-letter combinations can be formed if the second letter must be a vowel (A, E, I, O, or U), and the third letter must be different from the first letter?
26x5x25 = 3,250
400
In my fencing club there are twice as many boys who are in high school as there are boys who are in middle school. Of the students in the club who are in middle school, there are three times as many girls as there are boys. Half of the girls who are in the club are in high school. If there are 72 people in my fencing club, how many are middle school boys?
8
400
We connect dots with toothpicks in a grid as shown in Figure 1.14. If there are 10 horizontal toothpicks in each row and 20 vertical ones in each column, how many total toothpicks are there?
430 toothpicks
Hint:
How many rows are there? (The answer’s not 20.)
20x11 =220 vertical
21x10 = 210 horizontal
400
Which integers 
satisfy 
and how
many such integers are there?
31 numbers
500
How many arrangements are there of the letters in the word ‘COUNT’?
5! = 120
500
Our basketball team has 12 members, each of whom can play any position. In how many ways can we choose a starting lineup consisting of a center, a power forward, a shooting forward, a point guard, and a shooting guard?
the answer is 
500
There are 360 people in my school. 15 take calculus, physics, and chemistry, and 15 don’t take any of them. 180 take calculus. Twice as many students take chemistry as take physics. 75 take both calculus and chemistry, and 75 take both physics and chemistry. Only 30 take both physics and calculus. How many students take physics?
110
500
There are 190 people on the beach. 110 are wearing sunglasses, 70 are wearing bathing suits, and 95 are wearing a hat. Everyone is wearing at least one of these items. 30 are wearing both bathing suits and sunglasses. 25 are wearing both bathing suits and a hat. 40 are wearing both sunglasses and a hat. How many people are wearing all three items?
10