Our Women (2015) -

( Nos femmes ), released in 2015, is a French comedy-drama that centers on a harrowing moral dilemma between three lifelong friends. Directed by Richard Berry , the film is an adaptation of a contemporary stage play by Éric Assous and features a powerhouse trio of French cinema veterans: Daniel Auteuil , Thierry Lhermitte , and Berry himself. Plot Summary and Conflict

: They must decide whether 35 years of friendship outweighs the gravity of a murder.

“It's a nice comedy about the friendship between three men facing a tragic situation... Auteuil, Berry, and Lhermitte are convincing and frankly very funny.” IMDb Our Women (2015)

: As they argue, the facades of their own seemingly perfect lives and marriages begin to crumble. Critical Perspective

The story unfolds over a single night when Max (Berry), Paul (Auteuil), and Simon (Lhermitte) meet for their regular card game. The evening takes a dark turn when Simon arrives distraught, confessing that he has just strangled his wife, Estelle, during a heated argument. He begs his two best friends to provide a false alibi to protect him from prison. ( Nos femmes ), released in 2015, is

This confession sparks an intense ethical debate between the men:

The film is often praised for the chemistry and convincing performances of its lead actors, who capture the nuances of "solid yet fragile" male bonds. However, because it is based on a play, much of the action is confined to a single location—Max's apartment—giving it a distinct theatrical feel that some viewers find engaging while others may find limited. Audience Perspectives “It's a nice comedy about the friendship between

“An ethical debate takes place that reflects on friendship and all kinds of human ties.” Rotten Tomatoes Our Women (2015)

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( Nos femmes ), released in 2015, is a French comedy-drama that centers on a harrowing moral dilemma between three lifelong friends. Directed by Richard Berry , the film is an adaptation of a contemporary stage play by Éric Assous and features a powerhouse trio of French cinema veterans: Daniel Auteuil , Thierry Lhermitte , and Berry himself. Plot Summary and Conflict

: They must decide whether 35 years of friendship outweighs the gravity of a murder.

“It's a nice comedy about the friendship between three men facing a tragic situation... Auteuil, Berry, and Lhermitte are convincing and frankly very funny.” IMDb

: As they argue, the facades of their own seemingly perfect lives and marriages begin to crumble. Critical Perspective

The story unfolds over a single night when Max (Berry), Paul (Auteuil), and Simon (Lhermitte) meet for their regular card game. The evening takes a dark turn when Simon arrives distraught, confessing that he has just strangled his wife, Estelle, during a heated argument. He begs his two best friends to provide a false alibi to protect him from prison.

This confession sparks an intense ethical debate between the men:

The film is often praised for the chemistry and convincing performances of its lead actors, who capture the nuances of "solid yet fragile" male bonds. However, because it is based on a play, much of the action is confined to a single location—Max's apartment—giving it a distinct theatrical feel that some viewers find engaging while others may find limited. Audience Perspectives

“An ethical debate takes place that reflects on friendship and all kinds of human ties.” Rotten Tomatoes Our Women (2015)

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?