Is it possible by rearranging the digits of 3255 to make a number that is not a multiple of 3?

For how many integers, n, in {1,2,....,20} is the tens digit of n^2 odd?

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A number from 1, 2, 3, …, 19 is said to be a follower of a second number from 1,
2, 3, …, 19 if either the second number is 10 to 18 more than the first, or the
first number is 1 to 9 more than the second. Thus 6 is a follower of 16, 17, 18,
19, 1, 2, 3, 4 and 5. In how many ways can we choose three numbers from 1, 2,
3, …, 19 such that the first is a follower of the second, the second is a follower
of the third, and the first is also a follower of the third?

 In how many ways can we divide the numbers 1, 2, 3, … , 12 into four groups,
each containing three numbers whose sum is divisible by 3?

A positive integer is divided by 5. The quotient and the remainder are recorded.
The same number is divided by 3. Again the quotient and the remainder are
recorded. If the same two numbers in different order are recorded, find the
product of all possible values of the original number

There are three positive integers. The first is a two-digit number which consists
of two identical digits. The second one is a two-digit number which consists of
two different digits, and its units digit is the same as that of the first number. The
third one is a one-digit number which consists of only one digit, which is the
same as the tens digit of the second number. Exactly two of these three numbers
are prime numbers. In how many different ways can the three positive integers
be chosen?

The sum of the digits of each of four different three-digit numbers is the same,
and the sum of these four numbers is 2015. Find the sum of all possible values
of the common digit sum of the four numbers

A rectangular sheet of paper  inches by 11 inches is folded and then taped so that one pair of opposite vertices coincide. What is the number of inches in the perimeter of the resulting pentagon? Express your answer as a decimal to the nearest tenth

How many of the factorials from 1! to 100! are divisible by 9?

What is the smallest integer value of  such that the function  has a domain of all real numbers?

The decibel is a unit used to describe the loudness of a sound. For every 20-decibel increase, a sound gets 10 times as loud. Normal conversation is about 60 decibels, and a loud rock concert is about 120 decibels. How many times as loud is a rock concert compared to normal conversation?

Zeus threw, on average, 12 lightning bolts per day in the month of March. During the first week in April, he averaged 15 lightning bolts per day. How many lightning bolts does Zeus need to throw per day on average for the rest of April to maintain a 12-bolt-per-day average over March and April? Express your answer to the nearest integer.

Gaylon starts writing down dates from January 1, 2018 onward as follows: 01012018, 01022018, 01032018, etc. What is the 2018th digit Gaylon writes down?

If a,b,c >0 and 
Prove that : 

Given two points A(1;-3), B(2;-6) and a function . How many tangent lines  of  that A and B have the same distance to ?

A perfect day is defined to be in the form mm/dd/yy where the specific day is a prime number. For instance, February 23, 2018 and April 7, 2018 are both perfect days. How many perfect days are there between January 1, 2018 and December 31, 2020, inclusive?

Find x,y such that: 

Let ABC be an acute angled triangle and CD be the altitude through C. If AB = 8cm and CD = 6cm ,find the distance between the midpoints of AD and BC. 

How many integer solutions are there to

? Explain why