Devils Night Party Manki Yagyo Final | Naga Portable

Back at the corner, the drum lies on its side. A shoe is missing, and a matchbook still warm to the touch. The cracked ceramic eye on the shrine sits empty now, only a ridge of gold where the glaze forgot to hold. The night has done its work. People go home with pockets full of small absolutions and maybe, for the first time in a while, a plan to call someone back.

Naga arrives third: a lanky silhouette wrapped in a coat patched with the insignias of every faded club in town. Their face is a map of small scars and softer smiles. They cradle the box like a newborn. When Naga speaks, their voice is low and even; it moves like the current beneath the drumbeat. devils night party manki yagyo final naga portable

The alley throbs with a low, rubbery bass, wet neon pooling on cracked asphalt. Above, the sky is a bruised bruise—no stars, just the smudge of city light. Tonight is Devils Night, when the city’s edges fray and ritual slips into the open like smoke. They call it the Manki Yagyo Final: Naga Portable — a last run, a traveling shrine that fits in a duffel, a tail of tongue and teeth stitched into a portable god. Back at the corner, the drum lies on its side

The ritual begins with a list. Not names—phrases. "The promise kept in the rain." "The one that left the window open." Each phrase is read aloud and then folded into smoke; a paper is burned and the ash fed to the portable shrine. People speak in fragments: confessions that are more confessionals than admissions. Laughter breaks between phrases, high and sharp, sometimes briefly childish, sometimes feral. The night has done its work

"It takes what you give it," Naga says. "It gives back a shape."

A volunteer steps forward. They have been coming every Devils Night since the time when the city was younger and the rents were lower. They fold a scrap of paper—on it is written a sentence that begins, I should have told you— and presses it to the shrine. Naga turns the key in an empty motion, as if unlocking memory itself. The box hums for a throat-beat and emits a scent like wet moss and the inside of an old theater. For a second, the crowd glances inward and sees not the past but the shadow of what could have been if decisions had been different: a face, a door, a missed train. Then the moment passes; the paper crackles, the smoke lifts, and the person exhales as if freed.

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Back at the corner, the drum lies on its side. A shoe is missing, and a matchbook still warm to the touch. The cracked ceramic eye on the shrine sits empty now, only a ridge of gold where the glaze forgot to hold. The night has done its work. People go home with pockets full of small absolutions and maybe, for the first time in a while, a plan to call someone back.

Naga arrives third: a lanky silhouette wrapped in a coat patched with the insignias of every faded club in town. Their face is a map of small scars and softer smiles. They cradle the box like a newborn. When Naga speaks, their voice is low and even; it moves like the current beneath the drumbeat.

The alley throbs with a low, rubbery bass, wet neon pooling on cracked asphalt. Above, the sky is a bruised bruise—no stars, just the smudge of city light. Tonight is Devils Night, when the city’s edges fray and ritual slips into the open like smoke. They call it the Manki Yagyo Final: Naga Portable — a last run, a traveling shrine that fits in a duffel, a tail of tongue and teeth stitched into a portable god.

The ritual begins with a list. Not names—phrases. "The promise kept in the rain." "The one that left the window open." Each phrase is read aloud and then folded into smoke; a paper is burned and the ash fed to the portable shrine. People speak in fragments: confessions that are more confessionals than admissions. Laughter breaks between phrases, high and sharp, sometimes briefly childish, sometimes feral.

"It takes what you give it," Naga says. "It gives back a shape."

A volunteer steps forward. They have been coming every Devils Night since the time when the city was younger and the rents were lower. They fold a scrap of paper—on it is written a sentence that begins, I should have told you— and presses it to the shrine. Naga turns the key in an empty motion, as if unlocking memory itself. The box hums for a throat-beat and emits a scent like wet moss and the inside of an old theater. For a second, the crowd glances inward and sees not the past but the shadow of what could have been if decisions had been different: a face, a door, a missed train. Then the moment passes; the paper crackles, the smoke lifts, and the person exhales as if freed.

Math Written Exam for the 4-year program

Question 1. A globe is divided by 17 parallels and 24 meridians. How many regions is the surface of the globe divided into?

A meridian is an arc connecting the North Pole to the South Pole. A parallel is a circle parallel to the equator (the equator itself is also considered a parallel).

Question 2. Prove that in the product $(1 - x + x^2 - x^3 + \dots - x^{99} + x^{100})(1 + x + x^2 + \dots + x^{100})$, all terms with odd powers of $x$ cancel out after expanding and combining like terms.

Question 3. The angle bisector of the base angle of an isosceles triangle forms a $75^\circ$ angle with the opposite side. Determine the angles of the triangle.

Question 4. Factorise:
a) $x^2y - x^2 - xy + x^3$;
b) $28x^3 - 3x^2 + 3x - 1$;
c) $24a^6 + 10a^3b + b^2$.

Question 5. Around the edge of a circular rotating table, 30 teacups were placed at equal intervals. The March Hare and Dormouse sat at the table and started drinking tea from two cups (not necessarily adjacent). Once they finished their tea, the Hare rotated the table so that a full teacup was again placed in front of each of them. It is known that for the initial position of the Hare and the Dormouse, a rotating sequence exists such that finally all tea was consumed. Prove that for this initial position of the Hare and the Dormouse, the Hare can rotate the table so that his new cup is every other one from the previous one, they would still manage to drink all the tea (i.e., both cups would always be full).

Question 6. On the median $BM$ of triangle $\Delta ABC$, a point $E$ is chosen such that $\angle CEM = \angle ABM$. Prove that segment $EC$ is equal to one of the sides of the triangle.

Question 7. There are $N$ people standing in a row, each of whom is either a liar or a knight. Knights always tell the truth, and liars always lie. The first person said: "All of us are liars." The second person said: "At least half of us are liars." The third person said: "At least one-third of us are liars," and so on. The last person said: "At least $\dfrac{1}{N}$ of us are liars."
For which values of $N$ is such a situation possible?

Question 8. Alice and Bob are playing a game on a 7 × 7 board. They take turns placing numbers from 1 to 7 into the cells of the board so that no number repeats in any row or column. Alice goes first. The player who cannot make a move loses.

Who can guarantee a win regardless of how their opponent plays?

Math Written Exam for the 3-year program

Question 1. Alice has a mobile phone, the battery of which lasts for 6 hours in talk mode or 210 hours in standby mode. When Alice got on the train, the phone was fully charged, and the phone's battery died when she got off the train. How long did Alice travel on the train, given that she was talking on the phone for exactly half of the trip?

Question 2. Factorise:
a) $x^2y - x^2 - xy + x^3$;
b) $28x^3 - 3x^2 + 3x - 1$;
c) $24a^6 + 10a^3b + b^2$.

Question 3. On the coordinate plane $xOy$, plot all the points whose coordinates satisfy the equation $y - |y| = x - |x|$.

Question 4. Each term in the sequence, starting from the second, is obtained by adding the sum of the digits of the previous number to the previous number itself. The first term of the sequence is 1. Will the number 123456 appear in the sequence?

Question 5. In triangle $ABC$, the median $BM$ is drawn. The incircle of triangle $AMB$ touches side $AB$ at point $N$, while the incircle of triangle $BMC$ touches side $BC$ at point $K$. A point $P$ is chosen such that quadrilateral $MNPK$ forms a parallelogram. Prove that $P$ lies on the angle bisector of $\angle ABC$.

Question 6. Find the total number of six-digit natural numbers which include both the sequence "123" and the sequence "31" (which may overlap) in their decimal representation.

Question 7. There are $N$ people standing in a row, each of whom is either a liar or a knight. Knights always tell the truth, and liars always lie. The first person said: "All of us are liars." The second person said: "At least half of us are liars." The third person said: "At least one-third of us are liars," and so on. The last person said: "At least $\dfrac{1}{N}$ of us are liars."
For which values of $N$ is such a situation possible?

Question 8. Alice and Bob are playing a game on a 7 × 7 board. They take turns placing numbers from 1 to 7 into the cells of the board so that no number repeats in any row or column. Alice goes first. The player who cannot make a move loses.

Who can guarantee a win regardless of how their opponent plays?