inclusionAI/Ring-lite-rl-data huggingface dataset:
Given vectors $\overrightarrow{a}=(\cos{35}^\circ,\sin{35}^\circ)$ and $\overrightarrow{b}=(\cos{65}^\circ,\sin{65}^\circ)$, find the angle between vector $\overrightarrow{a}$ and vector $\overrightarrow{b}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30^\circ}
An engineer is designing an engine. Each cycle, it ignites a negligible amount of fuel, releasing $ 2000 \, \text{J} $ of energy into the cubic decimeter of air, which we assume here is gaseous nitrogen at $ 20^\circ \, \text{C} $ at $ 1 \, \text{atm} $ in the engine in a process which we can regard as instantaneous and isochoric. It then expands adiabatically until its pressure once again reaches $ 1 \, \text{atm} $, and shrinks isobarically until it reaches its initial state. What is the efficiency of this engine?

[i]Problem proposed by B. Dejean[/i]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.33}
On the eve of the Spring Festival, a convenience store sold a batch of goods that were purchased at 12 yuan per piece at a price of 20 yuan per piece, selling 240 pieces per day. After a period of sales, it was found that if the price per piece was increased by 0.5 yuan, then 10 fewer pieces would be sold per day; if the price per piece was decreased by 0.5 yuan, then 20 more pieces would be sold per day. In order to achieve a daily sales profit of 1980 yuan for the goods, how much should each piece be priced?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{23}
Let $m \in \mathbb{R}$, the line $x + my = 0$ intersects with the line $mx - y - 2m + 4 = 0$ at point $P(x, y)$. Find the maximum distance from point $P$ to the line $l: (x-1)\cos\theta + (y-2)\sin\theta = 3$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3 + \sqrt{5}}
Evaluate the convergence and find the sum of the series:
\[ \sum_{k=0}^{\infty} \frac{\left(\frac{1}{2}\right)^{2 k+4} 4\left(\begin{array}{c}
2 k+3 \\
k
\end{array}\right)}{k+4} \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Determine the highest order of differentiability of the function $f(x)$ if the function $g(x) = \int_0^x f(y) (y - x)^4 \, dy$ is continuously differentiable six times.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
What is a necessary and sufficient condition for an $n \times n$ matrix $A$ over $\mathbb{C}$ such that $A^m \to 0$ as $m \to \infty$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\rho(A) < 1}
Find the smallest natural number \( N \) such that \( \frac{(N!)^2}{(2N - 1)!} \leq \frac{1}{25000} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11}
Find the other $x$-coordinate of the intersection between the curves $y = \log x$ and $y = \sqrt{1-x^2}$. What is this $x$-coordinate?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.4}
Consider the two points \( A(4,1) \) and \( B(2,5) \). For each point \( C \) with positive integer coordinates, we define \( d_C \) to be the shortest distance needed to travel from \( A \) to \( C \) to \( B \) moving only horizontally and/or vertically. For example, for the point \( C(3,4) \), we compute \( d_C \) as follows:

- To get from \( A \) to \( C \) moving only horizontally and/or vertically, we can move 1 unit to the left then 3 units up for a total distance of \( 1+3=4 \).
- The shortest path from \( C \) to \( B \) moving only horizontally and/or vertically is to move 1 unit left and then 1 unit up (or 1 unit up then 1 unit left) for a total distance of \( 1+1=2 \).

Thus, for \( C(3,4) \), we have that \( d_C = 4 + 2 = 6 \).

The positive integer \( N \) has the property that there are exactly 2023 points \( C(x, y) \) with \( x > 0 \) and \( y > 0 \) and \( d_C = N \). What is the value of \( N \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4036}
In triangle \(ABC\), the sides \(AC = 14\) and \(AB = 6\) are known. A circle with center \(O\) is constructed using side \(AC\) as the diameter, intersecting side \(BC\) at point \(K\). It turns out that \(\angle BAK = \angle ACB\). Find the area of triangle \(BOC\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{21}
Prankster Pete and Good Neighbor George visit a street of $2021$ houses (each with individual mailboxes) on alternate nights, such that Prankster Pete visits on night $1$ and Good Neighbor George visits on night $2$, and so on. On each night $n$ that Prankster Pete visits, he drops a packet of glitter in the mailbox of every $n^{th}$ house. On each night $m$ that Good Neighbor George visits, he checks the mailbox of every $m^{th}$ house, and if there is a packet of glitter there, he takes it home and uses it to complete his art project. After the $2021^{th}$ night, Prankster Pete becomes enraged that none of the houses have yet checked their mail. He then picks three mailboxes at random and takes out a single packet of glitter to dump on George’s head, but notices that all of the mailboxes he visited had an odd number of glitter packets before he took one. In how many ways could he have picked these three glitter packets? Assume that each of these three was from a different house, and that he can only visit houses in increasing numerical order.

Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1540}
Given that there are 5 balls in a pocket, among which there are 2 black balls and 3 white balls, calculate the probability that two randomly drawn balls of the same color are both white.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{3}{4}}
Consider the line $a+bt$ where $a,b>0$. Let $B(t)$ be Brownian motion and let $\tau=\inf\{t>0:B(t)=a+bt\}$ be the first hitting time of that line, with the understanding that $\tau=\infty$ if the line is never hit. Compute the probability that Brownian motion hits that line, i.e., $P(\tau<\infty)$. Express your answer in terms of $a$ and $b$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{e^{-2ab}}
When Dave walks to school, he averages $90$ steps per minute, and each of his steps is $75$ cm long. It takes him $16$ minutes to get to school. His brother, Jack, going to the same school by the same route, averages $100$ steps per minute, but his steps are only $60$ cm long. How long does it take Jack to get to school?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$18 \text{minutes}$}
Let \( f(m, n) = 3m + n + (m + n)^2 \). Find \( \sum_{m=0}^{\infty} \sum_{n=0}^{\infty} 2^{-f(m, n)} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4/3}
Find the number of positive integers $k \le 2018$ for which there exist integers $m$ and $n$ so that $k = 2^m + 2^n$.
For example, $64 = 2^5 + 2^5$, $65 = 2^0 + 2^6$, and $66 = 2^1 + 2^6$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{66}
In a trapezoid \(ABCD\), the diagonals \(AC\) and \(BD\) are mutually perpendicular, and \(\angle BAC = \angle CDB\). The extensions of the lateral sides \(AB\) and \(DC\) intersect at point \(K\), forming the angle \( \angle AKD \), which is equal to \(30^\circ\). Find the area of triangle \(AKD\) if the area of the trapezoid is \(P\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{ \frac{3}{2} P }
Evaluate the limit: \[ \lim_{n\to\infty}\int_0^{2\pi}\frac{n (t+1) \sin (t)}{t (n t+1)^2}\,dt \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Let's call a natural number "suitable" if it is the smallest among all natural numbers with the same sum of digits as it has. Find all suitable numbers that are exact squares of natural numbers.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1, 4, 9, 49}
The solution to the equation $$\sqrt {x^{2}+6x+10}+ \sqrt {x^{2}-6x+10}=8$$ is \_\_\_\_\_\_.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\pm \frac {4 \sqrt {42}}{7}}
4 men can check exam papers in 8 days working 5 hours regularly . what is the total hours when 2 men will check the double of the papers in 20 days ?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{320}
Find the number of values of $x$ such that the area of the isosceles triangle with sides $x$, $65$, and $65$ is a positive integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4224}
Fourteen friends met at a party. One of them, Fredek, wanted to go to bed early. He said goodbye to 10 of his friends, forgot about the remaining 3, and went to bed. After a while he returned to the party, said goodbye to 10 of his friends (not necessarily the same as before), and went to bed. Later Fredek came back a number of times, each time saying goodbye to exactly 10 of his friends, and then went back to bed. As soon as he had said goodbye to each of his friends at least once, he did not come back again. In the morning Fredek realized that he had said goodbye a different number of times to each of his thirteen friends! What is the smallest possible number of times that Fredek returned to the party?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{26}
A positive integer is said to be 'good' if each digit is 1 or 2 and there are neither four consecutive 1's nor three consecutive 2's. Let \( a_{n} \) denote the number of \( n \)-digit positive integers that are 'good'. Calculate the value of \(\frac{a_{10} - a_{8} - a_{5}}{a_{7} + a_{6}}\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
As shown in the figure, point $E$ is on the side $AB$ of rectangle $ABCD$ and point $F$ is on the side $BC$. Connect $CE$ and $DF$, which intersect at point $G$. If the area of $\triangle CGF$ is 2, the area of $\triangle EGF$ is 3, and the area of the rectangle is 30, find the area of $\triangle BEF$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{35}{8}}
A line is drawn through the midpoints of any two edges of the triangular prism $ABC-A_1B_1C_1$. How many such lines are parallel to the plane $ABBA_1$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
Compute the length of the segment tangent from the origin to the circle that passes through the points $(4,5)$, $(8,10)$, and $(10,25)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{82}}
若 $0<x<2$, 则函数 $y=x(4-2x)$ 的最大值为 $\sqrt{2}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{2}}
Evaluate the integral using the Cauchy integral formula, given that the integrand has a removable singularity within the contour.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
For $n \geq 3$, consider the set $V = \mathbb{C} \setminus \{1, 2, ..., n\}$. Determine if the automorphism group $Aut(V)$ is finite, and if so, find an upper bound for its order. Specifically, verify whether $|Aut(V)| \leq n!$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{|Aut(V)| \leq n!}
Determine the annihilator of the tensor $e_1 \wedge e_2 + e_3 \wedge e_4$ in the vector space $V = \langle e_1, e_2, e_3, e_4 \rangle$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\{0\}}
Given \(x, y, z \in (0, 2]\), find the maximum value of the expression

\[ 
A = \frac{\left(x^{3} - 6\right) \sqrt[3]{x + 6} + \left(y^{3} - 6\right) \sqrt[3]{y + 6} + \left(z^{3} - 6\right) \sqrt[3]{z + 6}}{x^{2} + y^{2} + z^{2}}
\]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Determine the radius of convergence of the function \( \frac{\sinh(z)}{z} \) about the point \( z = \pi \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\infty}
Determine the range of values of $b$ for which the random variables $X$ and $Y$ are dependent, given their joint density function $f_{X,Y}(x,y)$. Provide your answer as an interval or union of intervals.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(-\infty, 0) \cup (0, \infty)}
Calculate the surface area of the portion of the plane \(2x + y + 2z = 16\) that lies within the region bounded by \(x = 0\), \(y = 0\), and \(x^2 + y^2 = 64\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{24\pi}
Find the non-zero function \( q(x) \) that is orthogonal to all polynomials of degree less than or equal to \( n \) with respect to the weight function \( w(x) = \sqrt{1-x^2} \) over the interval \([-1, 1]\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{U_{n+1}(x)}
Given $2$ red and $2$ white balls, a total of $4$ balls are randomly arranged in a row. The probability that balls of the same color are adjacent to each other is $\_\_\_\_\_\_$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{["\\frac{1}{3}"]}
Determine the amortized time complexity for a series of n operations on a disjoint set data structure, given that all union operations are performed before any find operations.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{O(\alpha(n))}
Determine the Galois group of the polynomial \( f(x) = x^6 - 3x^3 + 2 \) over the field of rational numbers \( \mathbb{Q} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{S_3}
Coach $F$ of country $F$ plans to have players $A_{1}, A_{2}, \cdots, A_{7}$ participate in three practice matches, each lasting 90 minutes. At any given moment, only one player is on the field. The total playing time for $A_{1}, A_{2}, A_{3}, A_{4}$ must be divisible by 7, and the total playing time for $A_{5}, A_{6}, A_{7}$ must be divisible by 13. How many different possible allocations of total playing time are there, considering these conditions?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6401545566}
In the right triangle \(ABC\), a circle is constructed with \(AC\) as its diameter. The circle intersects side \(AB\) at point \(E\). Point \(G\) is on side \(BC\) such that segment \(AG\) intersects the circle at point \(F\). Given that segments \(EF\) and \(AC\) are parallel, \(BG = 2CG\), and \(AC = 2\sqrt{3}\), find the length of \(GF\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
How many integers $n$ have the property that there exist positive integers $a, b, c$ such that $a^n + b^n = c^n$? Provide your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Determine the condition that must hold between two real numbers $a$ and $b$ such that the equation \( \left(\frac{1+iz}{1-iz}\right)^n = a+ib \) has only real solutions for $z$. What is this condition?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{a^2 + b^2 = 1}
Evaluate the integral \( \int_{-\pi}^{\pi} \frac{\sin nx}{(1+2^x)\sin x} \, dx \) for \( n \in \mathbb{N} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\pi}{2} \left(1 - (-1)^n\right)}
In a base \( a \) numeral system, determine the number of digits such that any integer ending in this digit will have all of its positive integer powers also end in the same digit.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^{\omega(a)}}
Find the constant value of $g$ when $\varepsilon$ is small, given the equation:
\[3\sinc\left(-1+ \frac\varepsilon T \right)-3\sinc\left(1+\frac\varepsilon T\right)-\sinc\left(-3+\frac\varepsilon T\right)+\sinc\left(3+\frac\varepsilon T\right) = \frac\varepsilon g\]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{3T}{16}}
Teams A and B each have 7 players who compete according to a predetermined sequence in a Go relay match. Both teams start with their first player competing against each other, the loser gets eliminated, and the winner competes against the second player of the losing team, and so on, until one team's players are all eliminated. The remaining team wins. How many possible match sequences are there?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3432}
设集合 $S=\{1,2,3, \cdots, 10\}, S$ 的子集 $A$ 满足
$$
A \cap\{1,2,3\} \neq \varnothing, \quad A \bigcup\{4,5,6\} \neq S,
$$
这样的子集 $A$ 的个数为 $\qquad$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{888}
Find the probability density function (pdf) of the time of the first arrival, \( T_1 \), given that there are exactly two arrivals by time 1 in a Poisson process \((N_t, t \geq 0)\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2(1 - t)}
4. The continuation of the height $B H$ of triangle $A B C$ intersects the circumscribed circle around it at point $D$ (points $B$ and $D$ lie on opposite sides of line $A C$). The degree measures of arcs $A D$ and $C D$, not containing point $B$, are $60^{\circ}$ and $90^{\circ}$, respectively. Determine in what ratio the segment $B D$ is divided by side $A C$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{3}:1}
Determine the number of points at which a line in $\mathbb{CP}^n$, defined as a copy of $\mathbb{CP}^1$, intersects with $\mathbb{CP}^2$. Provide your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Determine whether the function \( f(x,y) = (1+x)^t(1+y)^{1-t} - x^ty^{1-t} \), where \( t \in [0,1] \), satisfies \( f(x,y) \geq 1 \) for all \( x, y \geq 0 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{f(x,y) \geq 1}
A square with side length $x$ is inscribed in a right triangle with sides of length $3$, $4$, and $5$ so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length $y$ is inscribed in another right triangle with sides of length $3$, $4$, and $5$ so that one side of the square lies on the hypotenuse of the triangle. What is $\dfrac{x}{y}$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$\dfrac{37}{35}$}
A block is released from point O on an incline where the x-axis is along the incline. The coefficient of friction varies as \( \mu = kx \) with \( k = \tan\theta \). Given that the acceleration of the block is \( g\sin\theta(1-x) \), find the maximum distance traveled by the block.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Six-digit integers will be written using each of the digits $1$ through $6$ exactly once per six-digit integer. How many different positive integers can be written such that all pairs of consecutive digits of each integer are relatively prime? (Note: $1$ is relatively prime to all integers.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{72}
Let \( f \) be a differentiable function satisfying \( f(x+y)=(f(x))^{\cos y}\cdot (f(y))^{\cos x} \) for all \( x,y \in \mathbb{R} \). Given that \( f(0)=1 \) and \( f'(0)=\ln 2 \), evaluate the integral \( \int_{\frac{\pi}{2}}^{\frac{17\pi}{2}} \frac{f(x)}{f(x)+f(\pi /2-x)} \, dx \) and find the value of \( k \) such that the integral equals \( k\pi \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Evaluate the integral \( \displaystyle \int_{\partial \mathcal{D}(0,2)} \frac{8z^2-8z+1}{4z^3-8z^2+z-2}dz \) using the residue theorem.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2\pi i}
A function f(x) defined on R satisfies f(0)=0, f(x)+f(1-x)=1, f(x/5)=1/2f(x), and f(x1) <= f(x2) when 0 <= x1 < x2 <= 1. Find the value of f(1/2007). Express your answer as a fraction in simplest form.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1/32}
Determine whether the iterative scheme \(X_{n+1}=\frac{1}{2}(X_n)(1+\frac{a}{(X_n)^2})\) converges with order 2, given that \(\theta\) is the solution where \(\theta^2 = a\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Consider a sequence of complex numbers lying in a sector with an angular width less than \( \pi \). If the sum of the real parts of the sequence converges for any two non-collinear directions in the sector, does the sum of the moduli of the sequence also converge? Answer 'yes' or 'no'.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{yes}
Find the value of \( k \in \mathbb{R} \) such that \[ \lim_{x \to 0} \frac{1 - \cos(kx)}{x^2} = \int_0^\infty xe^{-x} \, \mathrm{d}x. \]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\pm \sqrt{2}}
Determine whether the sequence \( \sqrt[n]{n!} \) converges or diverges as \( n \to \infty \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\infty}
Evaluate the integral \( \int_{-\infty}^0 \frac{dx}{(x-2)\sqrt{1-x}}. \)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-\dfrac{\pi}{2}}
Suppose $u \in H^1(\mathbb{R}^2) \cap C(\mathbb{R}^2)$. Determine whether $\limsup_{|x| \to \infty} u(x) = 0$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Evaluate the integral: $$\int_{0}^{1}\frac{\sin^{-1}\sqrt x}{x^2-x+1}dx$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\pi^2}{6\sqrt{3}}}
How many positive integer solutions does the following system of equations have?

$$
\left\{ \begin{array}{l}
\sqrt{2020}(\sqrt{a} + \sqrt{b}) = \sqrt{(c + 2020)(d + 2020)} \\
\sqrt{2020}(\sqrt{b} + \sqrt{c}) = \sqrt{(d + 2020)(a + 2020)} \\
\sqrt{2020}(\sqrt{c} + \sqrt{d}) = \sqrt{(a + 2020)(b + 2020)} \\
\sqrt{2020}(\sqrt{d} + \sqrt{a}) = \sqrt{(b + 2020)(c + 2020)}
\end{array} \right.
$$

Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{
45
}
The value of $\log_5{3125}$ is between which consecutive integers $c$ and $d$? Find $c+d$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11}
A plane intersects a rhombus through one of its sides, forming angles of \( \alpha \) and \( 2\alpha \) with the diagonals of the rhombus. Determine the acute angle of the rhombus.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{60^\circ}
A square in the $xy$-plane has area $A$, and three of its vertices have $x$-coordinates 2, 0, and 18 in some order. Find the sum of all possible values of $A$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1168}
Ned is an explosives specialist racing to deactivate a time bomb on the top floor of a building. The building has a certain number of flights of stairs to the top floor, and Ned can run up one flight of stairs in eleven seconds. The time bomb has 72 seconds left on the timer, and Ned has spent 165 seconds running up the stairs. Ned will have 17 seconds to diffuse the bomb when he reaches it. How many flights of stairs are there in the building?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}