Mathleague 12316 sprint 21-30

Selena counts the number of ways she can arrange 18 threes, 6 ones, and a 0 in a line. Talar counts

the number of ways she can arrange 19 threes and 6 ones in a line. What is Selena’s number divided

by Talar’s number?

Susana has a non-square rectangular garden of lily pads. If the number of lily pads in her garden is

24 times the sum of the number of lily pads in the length and width of the garden, what is the smallest

possible number of lily pads in Susana’s garden?

The square root of a positive whole number n is not a whole number and has exactly 2023 digits to the

left of the decimal point. However, the cube root of n is a whole number. Excluding leading and trailing

zeroes, how many of the digits of the smallest possible value of n are zero?

Tags

CCSS.8.EE.A.2

Let x, y, and z be single-digit positive whole numbers with xyz = 108. How many possibilities are there

for the ordered triple (x, y, z)?

Two six-sided dice are initially blank on all six faces. A total of six dots are painted on the 12 faces of

the dice, with each face having 0 or 1 dot. Assuming each face is equally likely to have a dot, what is

the probability that at least one of the two dice has a dot on its top face? Express your answer as a

common fraction.

The number 2022 is an example of a positive whole number whose non-zero digits are all powers of

2. What is the average of all such four-digit whole numbers?

Tags

CCSS.HSF.BF.A.2

Three numbers are selected at random with replacement from the set {1, 2, 3, 4, 5}. They are placed

in non-descending order with a ≤ b ≤ c, and the sum of b − a and c − b is calculated. What is the

probability that this sum is at most 2? Express your answer as a common fraction.