FACTORS
COUNTING
DIGITS
RANDOM
200

What is the 3rd largest factor of 627?

57

200

On Planet Cat, the only letters are C, A, and T.  A word is any sequence of no more than 4 letters, and repeats are allowed.  How many words are there on Planet Cat?   (Obviously a word can't have 0 letters!)

120

200

What is the units digit of 32025?

3

200

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

300

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, 77

300

How many distinct ways are there to arrange 5 identical white blocks and 3 identical red blocks in a straight line?

56

300

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

300

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

400

How many factors of 100,000,000 are not factors of 100,000?

45

400

How many 10-digit numbers have the sum of their digits equal to 3?

55

400

How many 9-digit numbers are there such that going from left to right the digits of the number get smaller?

10

400

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

500

Determine how many factors of N are perfect squares where N =  3! x 5! x 7!

30

500

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

500

Sarah writes out all numbers between 1 and 999. How many times did she write the digit 5?

300

500

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

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