## Todai Entrance Exam: Math 2017 – Problem 3

(1) (2) (3) (4) (5) From (1), we have:

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## Todai Entrance Exam: Math 2017 – Problem 3

## Todai Entrance Exam: Math 2019 – Problem 3

## Todai Entrance Exam: Math 2018 – Problem 3

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(1) (2) (3) (4) (5) From (1), we have:

(1) (2) The easy way: The projection of on is . So . The hard way: Let be the intersection between and . As the triangle ABC is symmetric with respect to the line , every point on has a corresponding point on . So: Note that as . (3) We [...]

Problem link (1) We prove and (note that and , I doubt if zero can be considered as an even number though). Base case: . if a red card was taken. if a white card was taken. So and are true for . Induction step: Let . if a red card was taken. if a [...]