problem stringlengths 17 6.98k | answer stringlengths 1 5.61k | score float64 0.3 0.8 |
|---|---|---|
You have 100 coins on the table. Among these coins, 30 coins have tails facing up, while the remaining coins have tails facing up. You must create two piles such as each pile contains the same numberof tails facing up coins. You may only touch the coins, but you may not turn over any coin. | x | 0.4 |
Consider the set $\mathcal{S} = \{00000, 11111, 22222, 33333, 44444\}$. How many 5-digit numbers in $\mathcal{S}$, all having the same digit, have the property in which the sum is 20?
It is given there is only one such number. | 44444 | 0.8 |
A car travels at an average speed \( v \) km/h during the first hour. After the first hour, the speed becomes \( 2v \) km/h. If the car completes 6 hours 40 min journey, how far in km, does the car cover? | \frac{37v | 0.8 |
A certain radioactive element decaying to another element takes \(5,730\) years, which is the exact amount it takes another element to double from \(5\) grams to \(10\) grams. If there were \(5\) grams to start, how many grams will there be after \(3 \times 5,730\) years? | 40 | 0.7 |
A certain product's production cost is $8,000. If you sell 50% as many units as you produce, what will be the total cost per unit? | 160 | 0.3 |
What is the product obtained when all odd numbers from 1 through 100,000,000, inclusive, each raised to the power 2020, is subjected to modulo 5 operation? | 1 | 0.8 |
In 2012, Paris Olympics were held in London. If this trend continues, what year will the Paris Olympics be held again in London? | 2028 | 0.3 |
A circular garden is enclosed within an equilateral triangular fence. If the side-lengths dfrac{sqrt3}{2} units, what is the area, in square units, covered covered oen turf excluding the triangular region within the fence?
Your task is to calculate the area covered oen turf, excluding the triangular region within the... | 2sqrt{3 | 0.4 |
Determine the maximum possible area, in square units, the 4 largest rectangles from the set given, given they have sides at integer values?
{5 x 6, 6 x 6, 4 x 5, 5 x 6, 7 x 9, 8 x 7, 4 x 5, 10 x 12, 5 x 6, 6 x 6, 3 x 4, 4 x 6, 5 x 7, 7 x 8, 9 x 11, 2 x 5, 4 x 5, 8 x 8, 6 x 7, 5 x 6, 9 x 10, 7 x 12, 11 x 13, 3 x 7, 5 x... | 599 | 0.6 |
A rectangular garden is to be enclosed on three sides using 100 meters in total, including 2 gates, each 2 meters wide. If the gate space is subtractable from the total boundary, what is the maximum area the garden could have?
Answer this step-by-step to find the maximum area. | 1152 square meters | 0.7 |
A person starts walking 15 miles per hour towards the east, they turn right at 60 degrees, what speed should they maintain to keep the same absolute speed? | 15 | 0.7 |
In the year 2023, in which country is the second largest deposit site located?
(Note: the answer is located in the table, answering key is the country, 5pt.) | Beijing | 0.3 |
Let's create an **advanced mathematical problem in trigonometric identities**:
Prove the identity:
\[\frac{1 - \cos x + \cos 2x}{\cos x + \cos 2x} = \frac{1 - \cos x}{\cos x}\]
Hint: Make use the double-angle identity: \(\cos 2x = 2\cos^2 x - 1\). | 1 | 0.4 |
A medieval castle's moat is 50 meters wide. A builder wants to create two walkways across the moat using stone paving. The first walk will start from the moat’s western bank, reach the midpoint, turn, return to the midpoint, but this time not straight back but at an equal displacement on the eastern side. The second wa... | 75 \text{ meters | 0.5 |
In 2023, what is the last two-digit prime number in the binary equivalent sequence starting from the year 2023? | 11 | 0.7 |
A scientist is designing an experiment to study the effects on plant growth in different types on nitrogen fertilizer. However, the scientist also discovers they have an unlimited supply on another nutrient, potassium. The scientist wants to make sure they have adequate control to ensure nitrogen fertilizers have the s... | potassium | 0.8 |
A circular swimming pool is 10 meters in diameter. If the depth is 2 meters along the whole pool, how many liters will be needed to completely refill it, assuming the pool is empty when you start?
(Note: 1 m^3 = 1000 liters)
(A) 1570 liters
(B) 3140 liters
(C) 15700 liters
(D) 31400 liters
(E) 157000 liters | 157000 | 0.7 |
A frog is at the base level on the ground at position 0. It makes 10 bounding bounces to increase from level 0 to level 1. Bounces 1 through 5 each increase the height level. Bounces 6 through 10 each increase the height level back to 0. If it makes another set to increase the level to 1, how many bounces does the frog... | 15 | 0.4 |
A shop sells two types light bulbs: LED bulbs which last 8 years each, fluorescent bulbs which last 4 years each. In the first year, the shop sells twice as many LED bulbs as fluorescent bulbs. After 2 years, what is the total number bulbs in use if the shop sold 200 fluorescent bulbs in the first year? | 400 | 0.3 |
What is the correct term in the sequence: 2, 4, 8, 16, 31, 62, ... ? | 124 | 0.3 |
Alice starts walking from her home to her friend's house, which is 10 miles away. She walks at her usual speed. When she is halfway to her friend's house, she looks at her watch. She decides to increase her speed so she only takes an additional 30% longer than her usual walking time. If the total walking time from home... | 10 | 0.3 |
A spacecraft is traveling through space at an average speed equal to the speed at which sound travels through air at 1000 km/h. If it were to accelerate at this speed, how many meters per second must the spacecraft initially accelerate to reach this speed in exactly 1000 meters?
Note: 1 km = 1000 meters. | 39.25 m/s² | 0.5 |
A certain type K motor is priced at $140. Is it cheaper or expensive compared to another type K motor, which is priced at $149.99? | cheepear | 0.5 |
In how many different orders could the string 'AABBCCDDEEF', consisting only uppercase letters A, B, B, ..., F, be re-arraged, such the the letters 'AABBCCDDEEF', is such arrangement possible. | 20,922,789,888,000 | 0.4 |
In the hypercube \( \mathbb{R}^3 \) equipped in the \( l_1 \) norm, the vertices consist in all the \( 8 \) vectors \( \pm e_i \) (\( i = 1, 2, 3 \)). Find the number \( N = N(d) \) consisting in the vertices which pairwise distances lead to an isoscelese isoscelese tringulo, such as the distances be \( \Delta = \Delta... | 8 | 0.3 |
In the quantum state $$|\psi\rangle = \frac{1}{\sqrt{3}}(|0\rangle - i|1\rangle + i|2\rangle)$$, what is the probability, when measured in the computational basis, to find the system in the state $$|2\rangle$$? | 1/3 | 0.7 |
Which planets in our solar system have moons?
There could be multiple correct choices. | Earth, Jupiter, Uranus, Neptune | 0.5 |
In the quantum mechanics problem-solving competition, there's this scenario: Imagine you're dealing cards from the following stack: hearts, spade ace, spade 2, spade 3, spade 4, spade 5, spade 6, spade 7, spade 8, spade 9, spade 10, diamond ace, diamond 2, diamond 3, diamond 4, diamond 5, diamond 6, diamond 7, diamond ... | 15/19 | 0.3 |
In the beginning, there were only three tribes in the small village: the tribes A, B, &C. The tribes B &C followed the same set pattern, but the tribal members in the first group kept quiet, so the outsiders could not understand it. After the wedding, the changes happened. Four members from each group joined each group... | 13 | 0.6 |
In the fictional country Zephyrland, the Zephyrian government mandates citizens to maintain at the minimum 40% iron intake from plant sources to promote overall well-rounded health. Kiki, following the guidelines meticulously, consumes food from plant sources amounting to 200 grams in one day, maintaining iron content ... | 15 | 0.4 |
In the village square, there's an ancient clock tower. One day, the hour hand breaks, but the hour hand's shadow on the ground still points accurately to the hour. If it's 15:00 hours, in what compass direction does the shadow point? | East | 0.7 |
John is driving to the store. He needs to drive 200 miles to get there. His car gets 25 miles per 100 grams to the side. If his car gets 2.5 gallons to the side, how many gallons will John need to use to get to the store? | 720 | 0.3 |
A rare, ancient book holds the secret to deciphering an ancient numerical code. The code is inscribed in the margins as: 27 + 5, but the symbols used to represent the numbers have been shifted. The book explains the following transformation rule: 'Every digit in the number is doubled, but the order is reversed.' With t... | 424 | 0.3 |
At which number do the sequences 3n^2 + 5n + 2, 2n^2 + 3n + 1, 4n^2 + 7n + 3 have their first common value greater than 1000?
Options:
A) 10
A) 15
C) 20
D) 25
Answer | n^2 + 2n + 1 = 0 | 0.4 |
In the 2020 NBA Finals, which team won the first two games, but eventually fell to the eventual NBA Finals winner?
In the 2020 NBA Finals, the Miami Heat won the first two games against the NBA Champion. The NBA team went on to win the NBA Finals. | 2-0 | 0.3 |
A rare collectible card set from the year 2000 had 120 cards originally. Every month, 25% fewer cards were added to the set. After 4 months, how many cards were in the set? | 38 | 0.4 |
A peculiar robot on an alien planet calculates the time needed to complete tasks using the equation \(T = 5n + 3n^2\). If the robot needs to execute three tasks back-to-back, what is the minimum time required if each task must be completed consecutive on the timeline?
Options:
A) 27 | 27 | 0.6 |
In the year 2050, Earth's population is projected to be 9 billion people. Assuming the average person consumes 3,000 calories per day, how many calories in total will Earth's population be consuming daily in 2050?
Solve this step-by-step. | 27,000,000,000,000 | 0.5 |
A mysterious island is shaped as an equilateral hexagon, each side 10 kilometers long. A treasure is buried beneath the center point, which is 5 kilometers from any corner. An adventurer starts at one corner. If they decide to walk 30 kilometers in the shortest possible route to dig up the treasure, how many different ... | 6 | 0.8 |
In the Cartesian coordinate system, point $A$ is located at $(3, 4)$. A circle centered at the origin $O$ intersects the coordinate axes at points $P$ on the $x$-axis, $Q$ on the $y$-axis, $R$ in the first to fourth quadrilateral, $S$ in the second to fourth quadrilateral, $T$ in the first to fourth quadrilateral, $U$ ... | 12 | 0.4 |
On planet Zog, there exists an unusual 6-faced cube-shaped meteorite. It only falls on days when the moon's phase is full, which happens every 25 days. If you start counting from the day you discover the first meteorite, what is the 100th day on which you will encounter this meteorite? | 2475th | 0.7 |
A group consists 15 people: 5 engineers, 5 doctors, 5 teachers, 5 lawyers. Among these, 3 engineers, 2 doctors, 1 teacher, 2 lawyers, 1 student graduated. You randomly choose 3 from the group. The group is not ordered, You need to find the probability, if you have 1 from each profession graduated. | 72/455 | 0.3 |
In the year 1800, the population density in England was 730 people per square mile. By 1900, the population density had doubled. If the area in England was 130,800 square miles in 1900, calculate the total population in England in 1900. | 191,168,000 | 0.3 |
Consider the sequence defined as $f(x) = x^2 - 2x + 3$. If $f(x) = f(4)$, what is the sum $x_1 + x_2$?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5 | 2 | 0.8 |
A mysterious signal is received from space, consisting only three letters: **H, K, Z.**
What does the sequence **KHZKHZKHZ... repeat ad infinitum mean if each letter corresponds to the next prime number starting from 2?
What is the 100th number in the sequence? | 3 | 0.6 |
In 2018, the world population was 7.6 billion. If every person owned exactly one Android phone at the beginning, how many Android phones were in the world at the beginning?
Answer the question after careful thought: | 7.6 billion | 0.4 |
In an experiment, two identical light bulbs labeled A100W-110v-110W-220v respectively, were connected in the following way: A100W-110v was connected to 110v power supply. At the same time, A100W-220v was connected to 220v power supply. Considering their characteristics, calculate how much power each light will absorb, ... | Light 100W-110v will absorb 100W, while the 100W-220v will absorb 400W. | 0.5 |
A sequence is defined as \(T_1 = 2, \quad 2T_{N+1} - 3T_N = -1\) if \(N\) is odd, \(2T_{N+1} - 3T_N = 1\) if \(N\) is even, \(N \geq 1\). Find the first six numbers in the sequence \(T_1, \,T_2, \,T_3, \,T_4, \,T_5, \,T_6\).
To find these numbers, you must follow the pattern from the given recurrence relations. Try no... | 2, \frac{5 | 0.6 |
A rare species is found only in the dense rainforest. A scientist studies the species, observing it on 125 days out 250 days, but to be sure, the scientist also finds 5 additional scraps. Assuming the scientist finds exactly the same average number on each day, what is the daily average number the scientist finds? | 0.52 | 0.8 |
A mysterious stone statue stands on the ancient island, guarded round the clock. The watchmen, who patrol the perimeter day in, day out, following the same pattern, all work one hour shifts. Avaricious, they sneak off every ten days to plant treasure at the same spot on the island, returning the next morning, undetecte... | 24 | 0.6 |
A certain planet in our solar system is almost twice as far from the sun as Earth is, yet it completes one orbit around the sun in just 1467 days. If the planet's orbital radius is \( x \) times Earth's, determine \( x \). | 2 | 0.5 |
A 3D cube is inscribed in sphere. The sphere is inscribed in another cube. A point \(P\) is located at the center common to all three shapes. If the radius \(r\) is 15 units, calculate the volume \( V \) using the right triangles.
What is the sum \( r + V \)? | 27,015 | 0.4 |
An ancient Egyptian architect is designing an obelispur. An obelispur is an obelispur-shaped pillar made from whole blocks. The architect decides to use three differently shaped pillars; one shaped as an equilateral hexagon, one as an octagon, one as nonagon. The architect wants to make the obelispur so it looks larger... | 26 | 0.5 |
In the number 345678, how many 7s need to be added to the 6 to make the result equal to 345678? | 1 | 0.6 |
A rectangle is inscribed in an ellipse defined parametricly as \(x = 6\cos(\theta)\) , \(y = 4\text{}\text{in}(\theta)\) . If the area \(A\) enclosed within the rectangle satisfies the equation A = 36 , find the value which when \( \theta = \frac{ \xi \theta + \xi \xi \xi \theta}{\xi\theta}\) is evaluated makes the val... | π | 0.3 |
A scientist is working on an experiment to determine the optimal conditions to cultivate extremophile organisms—specific micro- or macroscopic organisms able to survive in otherwise lethal environments. They identify two key factors: pH level in the growing solution, measured on the pH paper from A to Z, along an alpha... | 50°F | 0.8 |
A train is traveling at 72 km/hr towards an oncoming train. An oncoming train is traveling at 96 km/hr. When the two meet, they decelerate at 0.5 m/s² to come to an immediate halt. If the two trees planted 2000 meters from both the North Tower through the tip, 1000 meters in both the end is complete. How far do you tra... | 800 | 0.4 |
A rare earth mineral X is found in the western region, but due to the geopolitical tensions there, the supply chain is often disrupted, making it difficult to determine the exact quantity imported to the country. However, using the newly discovered mathematical model, it is possible to determine the import quantity in ... | 467 | 0.5 |
In the ancient Olympics, which span from 776 BC to 393AD, there were only three athletic competitions:
1. The Pentathlon
2. The Diobateia
3. The Stadium race
Each event had their respective points. Assume the table below accurately depicts the values.
| Event | Value |
|--------------- |------- |
| Pentath... | 21 | 0.8 |
An elliptic curve $C$ is given over the field $\mathbb{Q}$, defined as $C: Y^2 = X^3 + AX + B$. A rational point $(x, 0)$ on $C$ corresponds to an order $2$-torsion point, which is an element $2P$ such $\text{ord}(2P) = 2$. Given $2P = \left(\frac{-A}{2}, 0\right)$ on $C$, find the number $n$ such $C(\mathbb{Q})\simeq ... | 2 | 0.4 |
Consider the sequence defined as \( F_n = F_{n-1} + F_{n-2} \) starting from \( F_1 = 1 \) such as the Fibonacci Sequence but each index number \( F_n \) is also the \( F_n \)th power. Determine \( F_5 \). | 3125 | 0.3 |
In the world map, which country shares the most borders among the following: China, Brazil, India, Australia, France, Turkey, Zambia, Switzerland, or Belgium? | TURKEY | 0.8 |
In what year did the first successful powered flight take place? | 1883 | 0.8 |
Alice is planning to sell some homemade cookies at her local fair. She decides to charge $2.50 per cookie. If she sells 40 cookies in the first hour, 50 cookies in the second hour, 30 cookies in the fourth hour, how many hours in total does she need to sell cookies to reach her goal if she needs to make $600 from selli... | 6 hours | 0.5 |
A special species doubles in population every year, starting from 500 individuals. After three years, the species is discovered, which reduces the population to 25% due to immediate capture efforts. The population continues to double but is limited to an upper ceiling in the fourth year. The birth rate is 25% each mont... | 5 | 0.3 |
Ananya is choosing an outfit consisting solely out from colored shapes. She picks one color from the four options: blue, orange, purple, or green. She also selects one figure from these options: circle, square, or rectangle. In how many total number N combinations does she end up picking either the blue color or the sq... | 7 | 0.7 |
In the coordinate plane, point $A$ is at $(0, 0)$, point $C$ is at $(0, 8)$, point $M$ is at $(8, 0)$, point $P$ is at $(3, 0)$, point $O$ is at $(4, 0)$, point $R$ is at $(0, 4)$, point $D$ is at $(6, 0)$, point $N$ is at $(4, 4)$, point $Q$ is at $(5, 0)$, point $K$ is at $(3, 4)$, point $Y$ is at $(7, 4)$, point $S$... | 13 | 0.4 |
A spherical balloon is filled to 60% capacity. If the radius doubles, how many times the current volume is the new volume? | 8 | 0.7 |
What is the combirlation (\begin{pmcd} 15 \\ 8 \end{pmcd}) - \begin{pmcd} 15 \\ 6 \end{pmcd} modulo 17?
Here, \begin{pmcd}n\\r\end{pmcd} represents the combirlational coefficient: \begin{pmcd}n\\r\end{pmcd} = \frac{n!}{r! * \begin{pmcd}n-r\end{pmcd}!}. | 16 | 0.4 |
Consider the sequence defined as \( \{ s_n \} \) such the first 6 numbers in the sequence (\( s_1, s_2, s_3, s_4, s_5, s_6 \) ) have the values 2, 5, 9, 14, 20, 27 respectively. The sequence is derived from the rule \( s_{n+1} - s_n = 3n \) or \( s_{n+1} = s_n + 3n \) starting from \( s_1 = 2 \). Given this information... | 317 | 0.7 |
A group consisting solely composed entirely metallic elements combined through chemical bonding in arrangement in which their atoms possesses identical electrón configuration implies what compound substance type, hyper-aggressive, poisonous or the ability to unite metallic single atoms to create metallic compounds. | Metallic Compund | 0.3 |
A rectangular garden is enclosed on three sides, using both wire fencing at $5 per foot, which costs $600, along side $10 per foot chain-link fencing which costs $150, what is the perimeter, in feet, covered, given area is square feet? | 480 \text{ feet | 0.4 |
A 4-digit number is represented as $\overline{ABCD}$. If the square root is rounded to the nearest integer, the result is 111. However, if the square root is rounded to the nearest integer after adding 0.5, the result is 112. Find the number $\overline{ABCD}$. | 12321 | 0.4 |
An octahedromino is a shape created from two congruent, equilateral triangles. How many distinct octahedrominoes can be constructed, considering rotations and reflections? | 6 | 0.4 |
In a small village, there are 100 houses arranged in a straight line. Each house has a unique address number from 1 to 100. On a particular day, a villagen folk decide to repaint the house numbers. However, they only have enough paint to cover the digits 1, 2, 3, and 4. Any house number with a digit not in this collect... | 18 | 0.5 |
In a small town, there are exactly four barbers. Each barber's haircuts must be done every 4 days. If one barber decides to visit another barber for a haircut, how many times would the barber who visits have to visit before he can cut his own hair? Note that the barber who is visited also gets a haircut during the visi... | 3 | 0.3 |
Imagine you have an infinite, flat sheet of paper covered entirely with a square lattice, each square having a side length of 1 unit. Suppose you place a circular sticker with a radius of 0.5 units on the paper. What is the probability that the sticker does not cover any lattice lines? (Hint: Focus on the area of the s... | 0 | 0.5 |
In a small town, there are 100 houses arranged in a circular manner. Each house is connected to its two immediate neighbors, and each connection has a probability of 0.5 of being broken. What is the probability that there is a way to walk from any house to any house without ever using a broken connection? | 1 | 0.4 |
Consider the function $f(x) = 2x - 3$, and the point $P = (3, f(3))$. Determine the equation of the line that is tangent to the parabola $y = f(x)^2$ and also tangent to the line that is tangent to $y = f(x)$. Let the point of intersection of these two tangency lines be $Q$. Determine the area of the quadrilateral $PQQ... | 9 | 0.5 |
In a certain kingdom, there are two cities: City of Light and City of Shadow. Each year, every citizen in these cities moves to the opposite town. At the beginning of 2023, City of Light has 15,000 more people than City of Shadow. At the beginning of 2024, after the entire populace has moved between the cities, it is o... | 45,000 | 0.8 |
In a particular type of crystal, the arrangement of ions forms a lattice with each corner and each face of the cube. If this crystal has a total of 40 ions, how many ions are located in the center of the cube? | 24 | 0.3 |
In a certain town, there is a tradition to plant a new tree on the first day of each season. Each tree has a distinct type and only one tree of each type can be planted. There are 20 types of unique tree saplings available. How many possible combinations of new tree plantings are there for the four seasons in a year? | 116280 | 0.8 |
In a science lab, a student places a 100-kg block of ice on a friction-less surface. Attached to the block is a 50-kg mass connected via a pulley system. If the ice block and the mass are released from rest, how high will the 50-kg mass fall before it collides with the ground? Assume no heat losses during the fall and ... | 5\text{ meters | 0.7 |
Consider the function f(x) = 5x² - 2x - 7. If g(x) = f(f(x)), and f(k) = 0, for some real k, determine the sum of the absolute values of k and g(k). | 8.4 | 0.4 |
In a certain mathematical town, the number of apples, oranges, and bananas sold in a grocery store forms a geometric series. If the number of apples sold is 81 and the number of bananas sold is 3, how many oranges were sold?
Also, if the grocery store sold 216 fruits in total, how many oranges were sold? | 9\sqrt{3 | 0.4 |
An archaeologist has uncovered a cryptic message etched into an ancient stone tablet: \(3x_1 - 2x_2 = 5\). If \(x_2 = 2\), which value of \(x_1\) does the archaeologist decipher to uncover the secret symbol? | 3 | 0.8 |
On a 4x4 chessboard, how many ways can you place 4 distinct pawns such that no two pawns are on the same row or same diagonal? | 2 | 0.3 |
In a 12×12×12 cube, there are 144 layers of unit squares. If you draw a line segment from the center of the bottom face to the center of the top face, how many unit squares will this line segment pass through? | 33 | 0.6 |
In the game of Tetris, if you are playing optimally and you have just completed a clear of four lines, how many holes does the playfield have after the clear? | 0 | 0.8 |
Consider a mystical land inhabited only birds. These birds exhibit unique characteristics defined through a mathematical principle known only to select scholars called Avians. There are only two types of Avians in this land: Blue Avians, which are immortal and double in number every year, and Red Avians, which are twic... | 8 | 0.6 |
In a biology class, students are studying the effects of different environmental pressures on a species of fish. They decide to conduct an experimental study to observe how changes in water temperature impact the fish's reproduction rates. They have two tanks of the same size and fill each with 100 liters of water, one... | 100 | 0.4 |
On a 2D plane, there are 3 lines given in the form y = kx, y = -x, and y = m. Find m and k such that there is one and only one point of intersection (P). What is the value of y in this point P? | 0 | 0.8 |
Which animal, known for its highly social behavior and use of tools, is also capable of teaching and learning from each another, much in the same way humans do, and has been observed displaying a phenomenon known in scientific circles called ‘behavioral mimicry’, an ability that was previously thought to be unique to h... | parrots | 0.3 |
Consider a function \( f \) defined on the interval \([0, 1]\) such that \( f(0) = 0 \) and \( f(1) = 1 \). Furthermore, \( f \) satisfies the condition \( f\left(\frac{a+b}{2}\right) = \frac{f\left(\frac{a+b}{2}+c\right) - f\left(\frac{a+b}{2}-c\right))}{2} \) for any \( a, a+b, \) and \( 1 \) in \([0, 1]\) and \( 0 \... | 1 | 0.5 |
In a certain country, the government decides to implement a new rule for a long jump event. If the total jump length (in meters) of an elite jumper is expressed in base 6, the number of unique digits in that representation must be less than 4 for the jumper to qualify for the Olympics. Which of the following jumpers wi... | 234 | 0.3 |
In a unique number game, the number of ways to arrange $k$ distinct marvellous marigolds in a row is given to be the $k$-catenary number. Suppose you are given 5 catenary numbers in a row. What is the smallest possible number of marigolds needed to generate these 5 numbers?
a) 3 | 5 | 0.8 |
In a certain code language, ‘CAT’ is ‘DWB’ and ‘BOAT’ is ‘CPBS’. What is the code for the word ‘WING’ in this language? | XJHO | 0.4 |
In a certain town, there are 100 houses arranged in a row. Each house is either blue or yellow. It is known that no two adjacent houses can both be blue. If the first house is yellow, how many different ways can the 100 houses be colored? | 2^{99 | 0.4 |
In the following chessboard pattern, how many squares are not highlighted in a standard 8x8 chessboard?
[Chessboard diagram with alternating white and black squares] | 32 | 0.8 |
In a fictional country called Numercalania, every year the government declares a new tax percentage based on the last digit of the previous year's GDP (GDP expressed in billions of dollars). If the previous year's GDP ends in 2, the tax percentage is 10% plus 5% of the last digit. If the previous year's GDP ends in 7, ... | 11 | 0.4 |
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