Minecraft Math
(No calculator allowed)
In your inventory, there are 27 slots (not including hot bar). Each slot can hold 64 items (ignore exceptions). If you fill your inventory completely, how many total items would you have?
\(27\times64=1728\)
Your favourite kind of pizza from your favourite pizza place has been tied to a railroad, and a train is quickly approaching! There is a lock connecting the ropes together, and you must open it to free your friend! On the lock, a message says that to find the code, you must take the first five prime numbers (in order) and find the corresponding letters in the alphabet.
You have 30 seconds before the train hits the pizza.Code: BCEGK
At the grocery store, there is an angry customer yelling at the cashier. The customer originally had 6.00 apples that are each worth 12.62$ plus a 6.00% tax. Unfortunately, when the cashier is scanning the items, 2.00 apples fall off the counter and into the trash. The cashier adjusts the price to X price. Rounding to two decimal places, how many apples did the customer walk home with? (Do NOT forget your units)
The customer walks home with 4.00 apples.
Write the number 40 using roman numerals.
XL
Treat!
After going trick-or-treating, you open a bag of Doritos that somebody gave to you. You notice that one of the chips has been broken and now forms a perfect right-angled triangle. What is the name of the side that is opposite to the right angle?
The hypotenuse
(Calculator allowed)
In Alex's hotbar, the quantities of the first five items are \(\small7,9,10,11,18\), respectively. Which number is the average (mean) of the other four numbers?
11
Ethical dilemma!
(No calculator allowed)
An evil math genius has kidnapped you, and you are forced to place a bomb in one of two buildings filled with your childhood stuffed animals. You want to save as many stuffed animals as possible. One building has \(\sqrt{3}^{\sqrt{3}}\) stuffed animals (wear and tear has resulted in a non-whole number of stuffed animals) and the other building has \(\sqrt{5.2}\) stuffed animals. Which building should you place the bomb in (assuming you want the least number of casualties)?
The building with \(\sqrt{5.2}\) stuffed animals.
\(\sqrt{5.2}\approx 2.28\)
\(\sqrt{3}^{\sqrt{3}}\approx 2.59\)
(Calculator allowed)
Joseph's backyard is a 7m by 67m rectangle. He has a very intelligent dog: Bruno. Bruno starts his walk in one of the corners of the backyard. From the corner, he faces the longer side (fence) of the rectangle that is opposite himself. He does this in such a way that he can walk in a straight line for 10m to reach the side (fence) he was looking at. After reaching this fence, he then turns and walks 10m in a straight line and touches the side of the fence parallel to the one touched before. He continues this until he reaches the fence that is perpendicular to the last touched side of the fence. How many complete 10m straight lines can Bruno walk?
Bruno can walk 9 complete 10m straight lines.
When writing down numbers 1 through 1000 (ex. 32 \(\leftrightarrow\) Thirty Two) how many numbers contain the letter ‘a’ in their spelling?
1 number (1000 \(\leftrightarrow\) One Thousand)
Larger Treat!
Assume one of the faces of a piece of candy corn forms a triangle.
What is the sum of the internal angles of the triangle?
180 degrees
(Calculator allowed)
How many blocks would it take to build a basic 8 x 8 x 5 house where the ceiling, floor, and walls are all 1 block thick, and there is a 2 block vertical opening to act as a door?
210 blocks
\(2(8\times8)+2(8\times3)+2(6\times3)-2=210\)
Simplify without using your calculator:
\(\frac{26364}{6762}\)
\(\frac{4394}{1127}\)
(No calculator allowed)
When taking a 30 multiple choice test on trigonometry, you notice that you’re running low on time. You're about to start question 12 on the test and you have 30 minutes remaining. You start panicking and decide to calculate how many minutes you can spend on each question. In your calculations, you take account of time wasting tasks:
Making unnecessary calculations - 2 minutes
Putting your answers on the bubble sheet - 3 minutes
Writing down your name/drawing on the back - 5 minutes
Taking these facts into account, how much time should you spend per question in order to finish the test on time?
\(\frac{20}{19}\) minutes/question or 1.05 minutes/question
A digital clock shows the time 4:56. How many minutes will pass until the clock next shows a time in which all of the digits are consecutive and are in increasing order?
458 minutes
12:34
Trig!
A spooky Halloween laser is attached to the side of a haunted house and tilted toward the ground. The wall, the ground, and the beam of light form the sides of a right-angled triangle with the beam of light as the hypotenuse.
If the hypotenuse of the right-angled triangle is equal to 1, and one of the internal angles is equal to \(\small\theta\), how can the other 2 side lengths be described as functions of \(\small\theta\)?
One side will have a length of \(\small\sin{\theta}\) and the other will have a length of \(\small\cos{\theta}\)
(Unit Circle)
(No calculator allowed)
Assume a new mob called the "goobermonster" has been added to Minecraft. 2 loving goobermonsters will produce exactly 1 offspring after being alive for exactly 10 days. Goobermonsters cannot die and keep on reproducing every 10 days if they have a mate. Assume any 2 goobermonsters can mate with each other. How many days are needed for the goobermonster population to exceed 546 goobermonsters if the population starts at 2 goobermonsters (at time t = 0)?
150 days
There is a bookstore in Logicland that has some very interesting books. Some of these books are reference books that list lots of books related to a topic. For example, a reference book about brainrot memes lists many books about brainrot memes. Some reference books list themselves. For example, a reference book listing all books would list itself. Suppose there is a reference book that lists all reference books that do not list themselves. Does this reference book list itself? Explain your answer.
This is a paradox.
The reference book lists itself if and only if it does not list itself. (contradiction)
(No calculator allowed)
The tire of a kids toy tricycle has 16 spokes that are distributed evenly throughout the tire. In addition, the circumference of the tire is 0.314 m. Using the information given, calculate the area in between two spokes that are next to each other. (Round \(\pi\) to 3.14). Round your answer to 4 decimal placements.
0.0005 m2
On Monday, Ronald McDonald travelled \(x\) km at a constant speed of 90 km/h. On Tuesday, he travelled on the same route at a constant speed of 120 km/h. His trip on Tuesday took 16 minutes less than his trip on Monday. The value of \(x\) is...
96
Big Treat!
(No calculator allowed)
When looked at from above, smarties are circular in shape with a diameter of approximately 15 mm. If you were laying out 267 smarties (your Halloween haul), how much area would your smarties cover when looked at from above? If 2 (singular) smarties cost $0.14 together, what is the cost per unit area of smarties? Round all answers to one decimal place and be sure to include units. (Make sure to use enough digits of \(\pi\))!
47182.8 mm2
0.0 dollars per mm2
(\(\small3.961...\times\space10^{-4}\) dollars per mm2)
(Calculator allowed)
Steve has spent a lot of time mining diamonds in the mines, and now he wants to prove to his dog Dennis that he knows math. Dennis hands him a piece of paper and tells him to fully expand the polynomial. Given the expression below, what answer should Steve get?
\((3x^2+2x+2)^2(x-7)\)
\(9x^5-51x^4-68x^3-104x^2-52x-28\)
(No Calculator)
Simplify the expression below so that it reaches the form of \(3^{\frac{a}{b}}x^{\frac{c}{d}}\)
\(\frac{3((\frac{1}{x})^{-32})^{\frac{1}{4}}}{\sqrt[\frac{23}{4}]{x^{\frac{-5}{6}}\cdot \frac{1}{3}x^{\frac{-6}{7}}}}\)
\(3^{\frac{27}{23}}x^{\frac{4006}{483}}\)
(Potentially with a domain restriction)
(No calculator allowed)
In a particular egg, when measuring the farthest possible points between the shell, you get a length of 7.6 cm. In addition you find that the total volume of the egg is 68 cm3. The yolk of the egg (a perfect sphere) happens to have a diameter that is a quarter of the longest length between the shell. Find how many times smaller the volume of the yolk is compared to the volume of the egg white (the rest of the egg that is not the yolk) (Round \(\pi\) to 3.14). Answer as a whole value or as a percentage.
18 times smaller
Suppose that \(\small p\) and \(\small q\) are two different prime numbers and that \(\small n = p^2 q^2\). The number of possible values of \(\small n\) with \(\small n<1000\) is…
7
Trig!
(No calculator allowed)
Legend says that a full moon causes the magical and mysterious mathematician to turn into a matherewolf (mathematician werewolf). Some townspeople call these wolves \(\Sigma\) wolves because of their amazing mathematical ability. Assume a full moon is a perfect circle with a radius of \(\pi\). What equation using the variables \(x\) and \(y\) on a Cartesian coordinate system can be used to represent this circle? Give four exact value solutions to this equation.
\(x^2+y^2=\pi^2\)
\((\pi, 0),(-\pi, 0),(0, \pi),(0, -\pi)\)
(and more)