Today is day three of the problem of the week. Before I begin the problems, I would like to explain one thing, which will be used throughout the medium and hard problems. You might not have learned it in school, but the concept is very simple.

A floor function is the largest integer less than or equal to a given number. For example, the floor function of 6.7 is 6. The floor function of 4.973 is 4. The floor function of π is 3. Basically, if you round the number down to the nearest whole, you will have its floor function.

Similarly, a ceiling function is the smallest integer greater than or equal to a given number. So, the ceiling function of 6.7 is 7. The ceiling function of 4.973 is 5. The ceiling function of π is 4. While rounding down yields the floor function, rounding up gives the ceiling function.

Normally, this is denoted by a special sort of bracket. Since I don’t know how to type these brackets into the computer, I will use the following notation:

floor(x) = the floor function of x

ceiling(x) = the ceiling function of x

This is an easy way to eliminate fractions and decimals from numbers to make the problems slightly easier and more realistic.

Good luck!

Easy:

What is the Least Common Multiple of

*f*,*g*, and*h*? Use the letter*j*to denote the answer.*j*= ____

Medium:

What is the number of dots in a regular (

*f*_{4}-*f*_{2})-gon array whose sides are of length (*f*_{1}-*f*_{3})?*n*= ____

Hard:

Find the explicit formula for the following sequence:

*v*,

*t*,

*s*, floor((

*g*+

*f*)/10), (

*g*- 60)/2,

*d*- 2, ...

The formula should be of the form

*ax*^{2}+*bx*+*c*. So, write your answer in terms of the value of coefficients*a*,*b*, and*c*.*a*= ____

*b*= ____

*c*= ____

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