Sharing your mathematics in MathYouLike

How many integer solutions are there to

$\frac{xy}{z}+\frac{xz}{y}+\frac{yz}{x} = 6$ ? Explain why

What is the value of $t^{-1}(64)$ where $t(3)=1$ and $t(2x)=2f(x)$

We have a triangle $\triangle ABC$ such that $AB = AC = 8$ and $BC = 10.$ What is the length of the median $AM$ ?

What is the smallest possible perimeter, in units, of a triangle whose side-length measures are consecutive integer values?

A triangle $\triangle ABC$ with $\angle A = 14^\circ$ is inscribed in a circle where $AB$ is a diameter. How many degrees are in $\angle B$ ?

Let $\triangle ABC$ be a right triangle such that $B$ is a right angle. A circle with diameter of $BC$ meets side $AC$ at $D.$ If the area of $\triangle ABC$ is $150$ and $AC = 25,$ then what is $BD$ ?

$a, b, c$ , and $d$ are drawn in the coordinate plane. $a = (0, 0), b = (5, 7), c = (3, 2)$ , and $d = (-3, -1)$ . A point $p$ is drawn, such that the average of $\overline{ap}, \overline{bp}, \overline{cp}$ , and $\overline{dp}$ is the least. What is $p$ ? Express your answer has a pair of coordinates.

There is a unit cube, with $6$ painted inscribed circles on each side. There are cones sticking out, inside the cube. The bases of the cones are the $6$ painted circles. The cones touch each other exactly in the center of the cube. A sphere is then inscribed in each of the $4$ created quadrants. What is the volume of one of the spheres? Express your answer as a radical, common fraction, and in terms of $\pi$ .

Papa John's pizza makes $40$ pizzas per day. $\frac{1}{4}$ of them have $20$ pepperoni and $10$ olives, and the other $\frac{3}{4}$ of them have $15$ pepperoni, $5$ salami, and $10$ olives, how much does Papa John's have to pay to make each day's worth of pizzas if pepperonis cost $1$ dollar per piece, olives cost $3$ dollars per $2$ pieces, and salami costs $7$ dollars per $5$ pieces?

Jimmy likes to throw darts, and Al likes to roll dice. If the dartboard has a fair chance of getting each of the values $1-10$ , but Al's dice has a $\frac{1}{n}$ probability of rolling $n$ , what is the probability that Jim's number will be greater than Al's number if Al is rolling a $10$ sided die? Express your answer as a common fraction.

Yvonne's musically musical music children are making a $8$ note song. The notes that the song can be in are the letters "a-z". Yvonne thinks a song is "Acceptable", if either the first or third, is a vowel. Yvonne's friend thinks a song is "Acceptable", if the first and second notes are either consecutive letter, or both vowels. What is the absolute different between the number of Yvonne's friend's "Acceptable" songs, and Yvonne's "Acceptable" songs?

Find the sum of all possible values of $x$ in this equation: $(x^2 - 5x + 6)(x^2 - 5x + 4)^{(x^2 - 1x + 6)} = 0$ .

Ren has a flute. It has $10$ consecutive sections, numbered from $1-10$ . He has $4$ colors of paint: red, green, blue, and yellow. He then paints every $2^{nd}$ section red, starting with the $2^{nd}$ section, then paints every $3^{rd}$ section green, starting with the $3^{rd}$ section, and so on, until he paints every $5^{th}$ section yellow. He repeats this procedure $2018$ times. At the end, how many sections are blue? Assume he can paint over a color with another color.

Call a "funky" number a number that is a multiple of a power of $3$ . How many funky numbers are there from $1$ to $2018$ ?

The roots of the equation $2x^2-mx+n=0$ sum to 6 and multiply to 10. What is the value of $m+n$ ?

Benito has 20 small balls of different colours: yellow, green, blue and black. 17 of the balls are not green, 5 are black, 12 are not yellow. How many blue balls does Benito have?

Betty likes calculating the sum of the digits that she sees on her digital clock (for instance, if the clock shows 21:17, then Betty gets 11). What is the biggest sum she can get if the clock is a 24-hour clock?

Tom has 9 bills of 100 euro, 9 bills of 10 euro, and 10 coins of 1 euro. How many euro does he have in total?

Which is the smallest positive integer divisible by 2, 3, and 4?

How many integers can one find in the interval from 2.09 to 15.3?