Episode 05: Igo — To Japan

The journey begins when Carly, Sam, and Freddie are nominated for the prestigious in Tokyo, Japan. Due to travel complications and Spencer trading their first-class tickets for five lower-class ones, the group—accompanied by Freddie's overprotective mother, Mrs. Benson—ends up flying to Japan in a cargo plane filled with possums. Their entrance into the country is anything but standard: they are forced to skydive into Tokyo after the pilot refuses to land. Sabotage and Survival

The group is eventually reunited thanks to a GPS tracking chip Mrs. Benson had secretly implanted in Freddie's head as a child. Victory Against the Odds Episode 05: iGo to Japan

is the first movie-length special of the Nickelodeon series iCarly , serving as a three-part event that officially counts as Season 2, Episode 5 . Released in November 2008, the 71-minute television film follows the Seattle-based web show crew as they travel across the world for their first major international recognition. The Great Pacific Adventure The journey begins when Carly, Sam, and Freddie

The antagonists drive Carly, Sam, and Freddie to a remote highway and abandon them, hoping they will miss the awards ceremony. Their entrance into the country is anything but

Kyoko and Yuki lure Spencer and Mrs. Benson to a spa where they are bound in seaweed wraps.

Upon arrival, the team meets their competitors, , who initially appear friendly but are secretly plotting to sabotage iCarly to ensure their own victory.

Desperate to enter the studio despite a language barrier and security guards who won't let them in, Freddie manages to hack the awards show's jumbotron. He broadcasts a live feed of Carly and Sam backstage frantically acting out their ordeal to the security guards. The audience finds the performance hilarious, and iCarly wins the award for . Kyoko and Yuki are ultimately arrested for their kidnapping and sabotage attempts. Production and Trivia

Written Exam Format

Brief Description

Detailed Description

Devices and software

Problems and Solutions

Exam Stages

The journey begins when Carly, Sam, and Freddie are nominated for the prestigious in Tokyo, Japan. Due to travel complications and Spencer trading their first-class tickets for five lower-class ones, the group—accompanied by Freddie's overprotective mother, Mrs. Benson—ends up flying to Japan in a cargo plane filled with possums. Their entrance into the country is anything but standard: they are forced to skydive into Tokyo after the pilot refuses to land. Sabotage and Survival

The group is eventually reunited thanks to a GPS tracking chip Mrs. Benson had secretly implanted in Freddie's head as a child. Victory Against the Odds

is the first movie-length special of the Nickelodeon series iCarly , serving as a three-part event that officially counts as Season 2, Episode 5 . Released in November 2008, the 71-minute television film follows the Seattle-based web show crew as they travel across the world for their first major international recognition. The Great Pacific Adventure

The antagonists drive Carly, Sam, and Freddie to a remote highway and abandon them, hoping they will miss the awards ceremony.

Kyoko and Yuki lure Spencer and Mrs. Benson to a spa where they are bound in seaweed wraps.

Upon arrival, the team meets their competitors, , who initially appear friendly but are secretly plotting to sabotage iCarly to ensure their own victory.

Desperate to enter the studio despite a language barrier and security guards who won't let them in, Freddie manages to hack the awards show's jumbotron. He broadcasts a live feed of Carly and Sam backstage frantically acting out their ordeal to the security guards. The audience finds the performance hilarious, and iCarly wins the award for . Kyoko and Yuki are ultimately arrested for their kidnapping and sabotage attempts. Production and Trivia

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?