FACTORS
What is the 3rd largest factor of 627?
57
On Planet Cat, the only letters are C, A, and T. A word is any sequence of no more than four letters, and repeats are allowed. How many words are there on Planet Cat?
120
What is the units digit of 32025?
3
Thomas was asked how old he is. He said, "In two years I will be twice as old as I was five years ago." How old is Thomas?
12
When 391 is divided by a positive two-digit number N, the remainder is 6. Find all the possible values of N.
11, 35, 55, 7
How many distinct ways are there to arrange 5 identical white blocks and 3 identical red blocks in a straight line?
56
In the equation AT + AT + AT = BAT, the same letter always stands for the same digit, and different letters stand for different digits. What is the 3-digit number BAT?
150
A graph has 11 vertices. Each vertex is connected to exactly k other vertices. How many different values of k are possible, if we know k is greater than 0?
5
How many factors of 100,000,000 are not factors of 100,000?
45
My local pizza restaurant offers 10 different pizza toppings. How many different types of pizza can I order that have at least 2 toppings? (Remember order doesn’t matter in pizza toppings).
1013
How many 9-digit numbers are there such that going from left to right the digits of the number get smaller?
10
There are 26 kids at a party and together they eat a total of 100 slices of pizza. Alice ate 1 slice, Ben ate 2 slices, Christina ate 3 slices, and Zach ate more slices than anyone else. What is the smallest number of slices that Zach could have possibly eaten?
6
Determine how many factors of N are perfect squares where N = 3! * 5! * 7!
30
How many 10-digit numbers have the sum of their digits equal to 3?
55
Sarah writes out all numbers between 1 and 999. How many times did she write the digit 5?
300
How many two-digit numbers give a perfect square when added to their “mirror” (the two-digit number written with its digits in reverse order)? For example, if you add 93 and 39 you get 132, which is not a perfect square.
8