inclusionAI/Ring-lite-rl-data huggingface dataset:
What is the largest finite number of roots that the equation 

$$
\left|x-a_{1}\right| + \cdots + |x-a_{50}| = \left|x-b_{1}\right| + \cdots + |x-b_{50}|
$$

can have, where \( a_{1}, a_{2}, \dots, a_{50}, b_{1}, b_{2}, \dots, b_{50} \) are distinct numbers?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{49}
Karen is constantly trying to stop the raccoons from getting in her trash. The first lock she tries stalls them for 5 minutes. The next lock stalls them for 3 minutes less than three times as long as the first lock. When Karen tries both locks at once, it stalled the raccoons for five times as long as the second lock alone. However, the raccoons are adapting to the locks, and with each attempt, they reduce the stall time of the first lock by 10% and the second lock by 15%. On the raccoons' third attempt to break through the locks, how long does it take them to get through both locks combined?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{43.35}
Find a positive integer that is divisible by 15 and has a square root between 33 and 33.5.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1110}
Given $a < 0$, and the terminal side of angle $\alpha$ passes through point $P(-3a, 4a)$, then $\sin\alpha + 2\cos\alpha = \_\_\_\_\_\_$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{2}{5}}
设方程(1+2+\cdots+k)-3(1+2+\cdots+t)=1的正整数解 (k,t) 按 k+t 从小到大排列为 (k_1,t_1), (k_2,t_2), \cdots. 求 k_6.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3196}
Let \(\omega=-\tfrac{1}{2}+\tfrac{1}{2}i\sqrt{3}.\) Let \(S\) denote all points in the complex plane of the form \(a+b\omega+c\omega^2,\) where \(0\leq a \leq 1,0\leq b\leq 1,\) and \(0\leq c\leq 1.\) Find the area of \(S.\) The original answer is in the form \(\frac{k}{m}\sqrt{n}\), please give the value of k + m + n.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
In covering a distance of 30 km, Arun takes 2 hours more than Anil. If Arun changes his speed, then he would take 1 hour less than Anil. Arun's speed is 5 km/h. What is the ratio of Arun's new speed to his original speed?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2:1}
Let \( A \) be a set containing only positive integers, and for any elements \( x \) and \( y \) in \( A \), \(|x-y| \geq \frac{x y}{30}\). Determine at most how many elements \( A \) may contain.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
Find the value of the sum $$\sum_{k=0}^n \frac{(-1)^k}{k!} \left(\sum_{m=0}^n \binom nm m^k\right)$$ where $n$ is a positive integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
数列 $\left\{a_{n}\right\}$ 满足: $a_{0}=\sqrt{6}, a_{n+1}=\left[a_{n}\right]+\frac{1}{\left\{a_{n}\right\}}$ (其中 $\left[a_{n}\right]$ 和 $\left\{a_{n}\right\}$ 分别表示实数 $a_{n}$ 的整数部分与小数部分), 则 $a_{2020}=a+\sqrt{b}$，求$a+b$的值。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6066}
设等差数列$\left\{ {{a}_{n}} \right\}$的前$n$项和为${{Sn}}$，且满足${{S}_{2017}}>0$，${{S2018}}<0$对任意$n\in {{N}^{*}}$，都有$\left| {{a}_{n}} \right|\ge \left| {{am}} \right|$，则$m$的值为__________．
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1009}
Find the number of positive integers less than $2018$ that are divisible by $6$ but are not divisible by at least one of the numbers $4$ or $9$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{280}
Let \( S = \{1, 2, \ldots, 98\} \). Find the smallest natural number \( n \) such that in any \( n \)-element subset of \( S \), it is always possible to select 10 numbers, and no matter how these 10 numbers are divided into two groups of five, there will always be a number in one group that is coprime with the other four numbers in the same group, and a number in the other group that is not coprime with the other four numbers in that group.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{50}
In trapezoid $ABCD$, where $AD \parallel BC$ and $\angle ABC + \angle CDA = 270^{\circ}$, compute $AB^2$. Given that $AB \cdot \tan(\angle BCD) = 20$ and $CD = 13$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{260}
Let \( n \) and \( k \) be positive integers such that \( k \geq n \) and \( k - n \) is an even number. We are given \( 2n \) lamps numbered from 1 to \( 2n \), each of which can be either on or off. Initially, all the lamps are off. We are considering a sequence of steps, where each step consists of changing the state of one lamp (from on to off or from off to on).

Let \( N \) be the number of sequences of \( k \) steps that result in the lamps numbered from 1 to \( n \) being on and the lamps numbered from \( n+1 \) to \( 2n \) being off.

Let \( M \) be the number of sequences of \( k \) steps that result in the lamps numbered from 1 to \( n \) being on and the lamps numbered from \( n+1 \) to \( 2n \) being off, and no lamps numbered from \( n+1 \) to \( 2n \) are ever turned on at any point in the sequence.

Determine the value of the ratio \( N / M \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^{k-n}}
A baker bakes 5 loaves of bread an hour in one oven. He has 4 ovens. From Monday to Friday, he bakes for some hours, but on Saturday and Sunday, he only bakes for 2 hours. The baker bakes 1740 loaves of bread in 3 weeks. How many hours does the baker bake from Monday to Friday?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25}
Let \( C \) be the circle with radius 1 and center at the origin. A point \( P \) is chosen at random on the circumference of \( C \), and another point \( Q \) is chosen at random in the interior of \( C \). What is the probability that the rectangle with diagonal \( PQ \), and sides parallel to the x-axis and y-axis, lies entirely inside (or on) \( C \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{4}{\pi^2}}
The perimeter of triangle \( \mathrm{ABC} \) is 1. A circle touches side \( \mathrm{AB} \) at point \( P \) and the extension of side \( \mathrm{AC} \) at point \( Q \). A line passing through the midpoints of sides \( \mathrm{AB} \) and \( \mathrm{AC} \) intersects the circumcircle of triangle \( \mathrm{APQ} \) at points \( X \) and \( Y \). Find the length of segment \( X Y \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{2}}
Bob's password consists of a positive single-digit number followed by a letter and another positive single-digit number. What is the probability that Bob's password consists of an even single-digit number followed by a vowel (from A, E, I, O, U) and a number greater than 5?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{40}{1053}}
Given 10 positive integers, the sums of any 9 of them take exactly 9 different values: 86, 87, 88, 89, 90, 91, 93, 94, 95. After arranging these 10 positive integers in descending order, find the sum of the 3rd and the 7th numbers.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{22}
A subscriber forgot the last digit of a phone number and therefore dials it randomly. What is the probability that they will have to dial the number no more than three times?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.3}
A ticket contains six digits \(a, b, c, d, e, f\). This ticket is said to be "lucky" if \(a + b + c = d + e + f\). How many lucky tickets are there (including the ticket 000000)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{55252}
将函数 $y=\sqrt{4+6 x-x^{2}}-2(x \in[0,6])$ 的图象逆时针方向旋转 $\theta(0 \leqslant \theta \leqslant \alpha)$, 得到曲线 $C$. 若对于每一个旋转角 $\theta$ ，曲线 $C$ 都是一个函数的图象，则 $\alpha$ 的最大值为多少？答案的形式为\arctan \frac{k}{m}，请给出k+m的值。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
Calculate the integral of the function $f(z) = \tan z$ around a rectangle in the complex plane with vertices at $0$, $2\pi$, $2\pi + 0.5i$, and $0.5i$. The rectangle extends from $0$ to $2\pi$ along the real axis and from $-0.5i$ to $0.5i$ along the imaginary axis.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-4\pi i}
On a table, there are three cones standing on their bases, touching each other. The radii of their bases are 10, 15, and 15. A truncated cone is placed on the table with its smaller base down, which has a common slant height with each of the other cones. Find the area of the smaller base of the truncated cone.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4\pi}
In a regular octagon inscribed in a circle of radius 1, if a point X is chosen on one of the diagonals such that it divides the diagonal in a 3:1 ratio, what is the absolute value of the product of the distances from X to all the vertices of the octagon?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Each term of a geometric sequence $\left\{a_{n}\right\}$ is a real number, and the sum of the first $n$ terms is $S_{n}$. If $S_{10} = 10$ and $S_{30} = 70$, then find $S_{4n}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{150}
已知正整数 n 的所有正因数排列为：1=d_1<d_2<d_3<\cdots，则在 1, 2, 3, \cdots, 2024 中使得 d_{10}=88 的所有数之和为__________.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2376}
Calculate: \(\left[\left(11 \frac{1}{9}-3 \frac{2}{5} \times 1 \frac{2}{17}\right)-8 \frac{2}{5} \div 3.6\right] \div 2 \frac{6}{25}\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{20}{9}}
Given the hyperbola equation x^2/16 - y^2/9 = 1 and point P(4, 4), count the number of lines that pass through point P and intersect the hyperbola at only one point. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Evaluate the following limit without using L'Hopital's rule: $$\lim_{x\to0} \frac{\ln(1+\sin^2(x))\cdot\cot(\ln^2(1+x))}{x^2}$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Find the order of the element $34 + \langle 18 \rangle$ in the factor group $\mathbb Z_{72} /\langle 18 \rangle$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Let $P$ be a square pyramid whose base consists of the four vertices $(0, 0, 0), (3, 0, 0), (3, 3, 0)$, and $(0, 3, 0)$, and whose apex is the point $(1, 1, 3)$. Let $Q$ be a square pyramid whose base is the same as the base of $P$, and whose apex is the point $(2, 2, 3)$. Find the volume of the intersection of the interiors of $P$ and $Q$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{27}{4}}
During intervals, students played table tennis. Any two students played against each other no more than one game. At the end of the week, it turned out that Petya played half, Kolya played a third, and Vasya played a fifth of all the games played during the week. How many games could have been played during the week if it is known that Vasya did not play with either Petya or Kolya?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30}
In a single-round-robin tournament, 10 chess players are participating. What is the minimum number of rounds after which a sole winner can be determined prematurely? (In each round, the participants are paired.

Win - 1 point, draw - 0.5 points, loss - 0).

#
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
James earns $20 an hour while working at his main job. He earns 20% less while working his second job. He works 30 hours at his main job, during which he spends 5 hours working overtime at a rate of 1.5 times his regular pay. James works 15 hours at his second job, as it is half the hours of his main job. He also has a side gig on weekends where he earns a fixed amount of $100 per day.

At the end of the week, James uses some tax deductions worth $200, which reduces his taxable income. The IRS tax rate for James' income is 18% and the state tax rate is 5%. In order to calculate James' weekly take-home pay, consider his earnings from the main job, including overtime, his second job, side gig income, tax deductions, and the applicable taxes. How much does James take home per week?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\$885.30}
We have $2012$ sticks with integer length, and sum of length is $n$. We need to have sticks with lengths $1,2,....,2012$. For it we can break some sticks ( for example from stick with length $6$ we can get $1$ and $4$).
For what minimal $n$ it is always possible?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2012^2 - 2012 + 1}
There are numbers $1, 2, \cdots, 36$ to be filled into a $6 \times 6$ grid, with each cell containing one number. Each row must be in increasing order from left to right. What is the minimum sum of the six numbers in the third column?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{63}
Calculate the limit:

$$\lim_{n\to\infty} \frac{\left(\prod_{k=1}^n k^{k^p}\right)^{\frac{1}{n^{p+1}}}}{n^{\frac{1}{p+1}}}$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{e^{-\frac{1}{(p+1)^2}}}
Some eggs and 5 pounds of oranges are currently at the same price. If the price of eggs rises by 3 percent and the price of oranges rises by 6 percent, it will cost $8.999999999999986 more to buy the eggs and 10 pounds of oranges. How many eggs are we considering?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
If $A=\{ x | ax^2 - ax + 1 \leqslant 0, x \in \mathbb{R} \} = \emptyset$, then the range of values for $a$ is ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{[0,4)}
9. Given that two cars, A and B, start from points $A$ and $B$ respectively at the same time, and travel back and forth between $A$ and $B$ at a constant speed. If after the first meeting, car A continues to drive for 4 hours to reach $B$, while car B only drives for 1 hour to reach $A$, then when the two cars meet for the 15th time (excluding meetings at points $A$ and $B$), they have driven $\qquad$ hours.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{86}
Given that odd prime numbers \( x, y, z \) satisfy
\[ x \mid (y^5 + 1), \quad y \mid (z^5 + 1), \quad z \mid (x^5 + 1). \]

Find the minimum value of the product \( xyz \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2013}
What is the sum of the infinite series $$1+ {1\over 11}+ {1\over 111}+ {1\over 1111}+....$$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$\frac{10}{9}$}
Three chords are drawn from point $M$ on a circle: $MN=1$, $MP=6$, and $MQ=2$. The angles $NMP$ and $PMQ$ are equal. Find the radius of the circle.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2 \sqrt{\frac{34}{15}}}
已知椭圆的两个焦点和中心将准线之间的距离四等分, 则该椭圆一个焦点与其短轴两端点连线的夹角度数为 $\qquad$ .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$90^{\circ}$}
A boss plans a business meeting at Starbucks with the two engineers below him. However, he fails to set a time, and all three arrive at Starbucks at a random time between 2:00 and 4:00 p.m. When the boss shows up, if both engineers are not already there, he storms out and cancels the meeting. Each engineer is willing to stay at Starbucks alone for an hour, but if the other engineer has not arrived by that time, he will leave. What is the probability that the meeting takes place?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{7}{24}}
every second saturday and all sundays are holidays . how many working days will be there in a month of 30 days beginning on a saturday ?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{23}
Two cones have a common vertex, and the slant height of the first cone is the height of the second cone. The angle at the vertex of the axial section of the first cone is $\arccos \frac{1}{3}$, and of the second cone is $120^{\circ}$. Find the angle between the sides where the lateral surfaces of the cones intersect.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{60^\circ}
5. The distance between the centers $O_{1}$ and $O_{2}$ of circles $\omega_{1}$ and $\omega_{2}$ is $5 r$, and their radii are $r$ and $7 r$ respectively. A chord of circle $\omega_{2}$ is tangent to circle $\omega_{1}$ and is divided by the point of tangency in the ratio $1: 6$. Find the length of this chord.

( 7 points)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7r\sqrt{3}}
The numbers $1, 2, . . . , 1983$ stand at the vertices of a regular 1983-gon. Any of the axes of symmetry of the 1983-gon divides the numbers which do not stand at the vertices through which the axis passes (if any) into two sets: on either side of the axis. Let us call an arrangement of numbers good with respect to a given axis of symmetry if every number of one set is greater than the number symmetrical to it. How many such good arrangements exist with respect to any axis of symmetry? Please provide the number of such arrangements.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Let \( w \) be a complex number such that \( |w - 3 + 2i| = 4 \). Find the minimum value of
\[
|w + 1 + 2i|^2 + |w - 7 - 2i|^2.
\]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{48}
In the tetrahedron \(ABCD\), \(AD = 2\sqrt{3}\), \(\angle BAC = 60^\circ\), \(\angle BAD =\) \(\angle CAD = 45^\circ\); if a sphere tangent to plane \(ABC\) at point \(D\) and inscribed within the circumsphere of the tetrahedron has a radius of 1, find the radius of the circumsphere of tetrahedron \(ABCD\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Determine the largest real number $c$ such that for any 2017 real numbers $x_{1}, x_{2}, \ldots, x_{2017}$, the inequality $$\sum_{i=1}^{2016} x_{i}\left(x_{i}+x_{i+1}\right) \geq c \cdot x_{2017}^{2}$$ holds.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-\frac{1008}{2017}}
Determine the smallest positive real  $K$  such that the inequality
\[ K + \frac{a + b + c}{3} \ge (K + 1) \sqrt{\frac{a^2 + b^2 + c^2}{3}} \]holds for any real numbers  $0 \le a,b,c \le 1$ .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\sqrt{6}}{3}}
There is a 5-digit odd number $x$. By replacing all 2s in $x$ with 5s, and all 5s with 2s, without changing other digits, a new five-digit number, denoted as $y$, is obtained. If $x$ and $y$ satisfy the equation $y = 2(x + 1)$, find $x$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{29995}
Tom is cutting a piece of wood to make a shelf. He cut the wood to some length, but it is too long to fit in the bookshelf he is making. He decides to cut 25 cm off the board. But it turned out longer than the other boards, which were 125 cm long before he cut the 7 cm off. How long was the wood initially?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{143}
Divide 6 volunteers into 4 groups, with two groups having 2 people each and the other two groups having 1 person each, to serve at four different pavilions of the World Expo. How many different distribution schemes are there? (Answer with a number).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1080}
Determine the value of the infinite series $$\sum_{n=1}^{\infty}\frac{x^{2^{n-1}}}{1-x^{2^n}}$$ or $$\frac{x}{1-x^2}+\frac{x^2}{1-x^4}+\frac{x^4}{1-x^8}+\cdots$$ for $x\in\mathbb{R}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{x}{1-x}}
If $\alpha=3$, then the terminal side of $\alpha$ falls in the \_\_\_\_\_\_ quadrant.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{second}
50*. What is the greatest number of circles of radius 1 that can be placed on a plane so that they all intersect a certain fixed unit circle $S$ and no one of them contains the center of $S$ or the center of another circle inside it?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{18}
Let point P be a point on the ellipse $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$, $F_1$, $F_2$ be the left and right foci of the ellipse respectively, and $I$ be the incenter of $\triangle PF_1F_2$. If $S_{\triangle IPF_1}+S_{\triangle IPF_2}=2S_{\triangle IF_1F_2}$, then calculate the eccentricity of the ellipse. Express your answer as a numerical value.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{2}}
Compute the sum of all positive integers whose digits form either a strictly increasing or strictly decreasing sequence.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25617208995}
Given the polynomial p = x^4 + 6x^3 + 11x^2 + 3x + 31, find the number of integer values of x for which p is a perfect square. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
How many ordered pairs of positive integers \((x, y)\) satisfy the equation
\[ 
x \sqrt{y} + y \sqrt{x} + \sqrt{2006 x y} - \sqrt{2006 x} - \sqrt{2006 y} - 2006 = 0 ?
\]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
Find the number of ways in which the nine numbers $$1,12,123,1234, \ldots, 123456789$$ can be arranged in a row so that adjacent numbers are relatively prime.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Compute the number of five-digit positive integers whose digits have exactly  $30$  distinct permutations (the permutations do not necessarily have to be valid five-digit integers).

*Proposed by David Sun*
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9720}
According to national regulations, only adults aged between 18 and 70 are eligible to apply for a motor vehicle driver's license. A sixth-grade student, Li Ming, says, "My dad has a driver's license. His age equals the product of the month and day of his birth, and that product is 2975." How old is Li Ming's father?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{35}
A rectangular ceiling PQRS measures 6m by 4m and is to be completely covered using 12 rectangular tiles, each measuring 1m by 2m. A beam TU is positioned so that PT = SU = 2m, and no tile can cross the beam. Calculate the total number of possible arrangements of tiles. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{180}
The difference between $\frac{1}{3}$ of $x$ and $x$ is a positive number, expressed as an inequality is ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{-2}{3}x > 0}
4. To completely fit 4 steel balls with a radius of 1 into a container shaped as a regular tetrahedron, the minimum height of this regular tetrahedron is
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{["4+\\frac{2\\sqrt{6}}{3}"]}