brain

We are given a long sequence of integers, and we are allowed to pick a subsequence from it. The goal is not just to maximize the length of the subsequence, but to impose a very specific structural constraint on how the chosen elements repeat.

Digital transformation, platform economy, and the vocabulary of China's tech-society interface at C1 level

We start with a string s. We may delete exactly x characters, keeping the remaining characters in their original order. The resulting string is a subsequence of s. Inside that resulting string, we look for as many non-overlapping occurrences of a pattern p as possible.

間 (kan/ken/aida): interval. JLPT N5 kanji.

HSK 1 | noun | television, TV

Learn how to use 〜ざるを得ない (zaru wo enai) to express reluctant necessity — 'have no choice but to; can't help but do.' Includes structure, nuance, examples, and comparisons.

青 (blue, green): 8 strokes, JLPT N5. On: セイ、ショウ. Kun: あお、あお-い.

今 (now): 4 strokes, JLPT N5. On: コン、キン. Kun: いま.

Comprehensive N3 review: mock N3 reading passage with full analysis, 15 grammar transformation exercises, listening strategy guide, self-assessment checklist for all 10 lessons, and a Bridge to N2 preview.

HSK 5 | verb/noun | systematic improvement for better performance or efficiency

飲 (drink): 12 strokes, JLPT N5. On: イン. Kun: の-む.

The problem presents a keyboard with three rows of characters arranged exactly like a standard QWERTY layout. Mole is typing messages on this keyboard, but he accidentally shifted his hands either one key to the left or one key to the right.

We have a sequence of pillars arranged from left to right. Pillar i has height h[i]. A valid jump can only go forward, from a smaller index to a larger index, and the height difference between the two pillars must be at least d.

天 (ten/ame): heaven. JLPT N5 kanji.

HSK 4 | noun | a serious disease caused by uncontrolled cell growth

We are given a collection of exams, each with two relevant days. The official schedule assigns exam i a day ai, but the student has a special agreement allowing him to take it earlier on day bi, where bi < ai.

HSK 5 | noun | the specific purpose or role something is designed or able to perform

HSK 4 | noun / adjective | an organized set of connected parts, or thorough and orderly

The problem defines a linear sequence $fn$ with two initial values $x = f1$ and $y = f2$, and a recurrence that repeats every six terms: $f{n} = f{n-1} - f{n-2}$.

Learn 〜べく (formal purpose) and 〜べきだ/べきではない (moral/logical obligation) in formal Japanese writing and speech.

安 (cheap, peaceful): 6 strokes, JLPT N5. On: アン. Kun: やす-い.

Dialect variation in Sindarin: Gondorian Sindarin (influenced by Númenórean usage and Adûnaic), Mirkwood Sindarin (Silvan-influenced), and key phonological differences.

Learn 〜どころか (far from ~, let alone ~) — the N3 pattern for expressing strong unexpected contrast or reversal.

HSK 3 | adj/noun | polite behavior or manners

HSK 5 | noun | performance; capability; functional properties of a product or system

HSK 3 | noun | the host of a place or owner of something

HSK 4 | noun | a software application designed for a specific purpose

HSK 3 | noun | the meaning of a word or the idea behind something

Learn vocabulary and grammar for discussing Chinese traditional festivals, including the customs, foods, and activities associated with major celebrations.

Side-by-side comparison of HSK old standard (2.0, 6 levels) and new standard (3.0, 9 levels), including vocabulary counts, CEFR alignment, and transition timeline.

Complete JLPT N1 grammar reference: ~200 patterns including classical Japanese influences, literary forms, highly formal conjunctions, advanced conditionals, and nuanced distinctions separating N1 from N2.

HSK 4 | noun | a positive result obtained through effort

HSK 4 | adverb | doing something at the scheduled or required time

Master six essential Japanese patterns for expressing probability, hearsay, and inference — かもしれない, でしょう/だろう, はずだ/はずがない, らしい, そうだ (two uses!), and ようだ — with a certainty-scale comparison table.

HSK 1 | noun | informal word for father

安全な (あんぜんな / anzen na): safe. N4 level Japanese vocabulary.

Learn to talk about what you like doing and what skills you have using 喜欢 and 会.

〜ために: JLPT N4 grammar pattern. Usage, structure, examples, and comparison with similar patterns.

Learn how to compare people and things using 比, 没有, and 一样 in natural Chinese.

Critical thinking patterns in Chinese — the vocabulary and structures of analysis, evaluation, and reasoned judgment at C1 level

肉 (ニク): meat; flesh. JLPT N5 essential kanji.

We start with a single group containing all given numbers. Whenever Toastman receives a group, he adds the sum of all numbers in that group to the score. If the group contains more than one number, Appleman may split it into two non-empty groups and send both back to Toastman.

HSK 3 | preposition/conjunction | introduces a cause or reason, more formal than 因为

HSK 3 | verb / noun | to contact, to get in touch; connection, link, relationship

JLPT N4 kanji 路 — readings, vocabulary, stroke order, mnemonic, and common confusion pairs.

Sindarin object pronouns and the dative construction with an: direct object pronoun forms, indirect object, and attested examples.

Master Japanese passive (〜られる/〜れる), causative (〜させる/〜せる), and causative-passive (〜させられる) forms. Includes full conjugation tables for 10 verbs, the suffering passive, and three dialogues contrasting active/passive/causative perspectives.

HSK 3 | verb / noun | to perform, to put on a show; a performance, show

時 (ji/toki): time. JLPT N5 kanji.

HSK 4 | verb/noun | to infer, to speculate; inference, speculation

N1 grammar pattern 〜にほかならない: emphatic definitional assertion — X is nothing other than Y. Used for declarative identification, formal analysis, and rhetorical emphasis.

HSK 3 | adjective | free from stress or difficulty; comfortable and at ease

JLPT N4 kanji 仕 — readings, vocabulary, stroke order, mnemonic, and common confusion pairs.

HSK 3 | pronoun / adjective | another, other, separate — introduces a different item

HSK 6 | n | the meaning or significance contained within a word, phrase, or act

HSK 6 | verb | to draw conclusions through reasoning from available evidence

HSK 2 | verb | to feel or think based on personal impression; contrast with 认为 for reasoned opinion

HSK 3 | conjunction | not only — the first half of the 不但…而且… pattern

HSK 4 | noun | physical space, room, or conceptual space for something

HSK 1 | noun | weather

Learn 〜ざるを得ない to express unavoidable obligation — you have no choice but to do something, despite reluctance.

Learn 〜てからというもの to express a fundamental, sustained change that began at a specific turning point.

Engage with Chinese discourse on the ethical dimensions of technology, including AI ethics, privacy, data security, and algorithmic bias.

HSK 5 | noun | the aggregate of people living together in a structured community

HSK 3 | conjunction | adds an additional point to what was already stated

HSK 3 | noun | tree; also used in compounds for planting or establishing

Master Japanese reported speech patterns — 〜と言う, 〜と思う, 〜と聞く, 〜によると, 〜そうだ — and learn to convert direct speech to indirect speech with correct plain-form usage before と.

HSK 3 | adjective | ordinary, common, average — not special

HSK 2 | adverb / adjective | intensifier meaning 'especially' or describing something as unique

HSK 3 | adverb | approximately, probably, roughly — an estimate rather than exact figure

HSK 5 | noun phrase | the portion of a market controlled by a company or product

HSK 5 | verb/noun | blending of distinct elements into a unified whole

HSK 5 | verb | to show the way or help someone develop in a certain direction

N1 grammar pattern 〜に反して/〜に反する: expressing that something is contrary to an expectation, rule, principle, or agreement. Legal and formal register.

HSK 4 | noun | physical force pressing on something, or mental/social stress

HSK 3 | adverb | after all — points to an underlying truth or fundamental reason

HSK 4 | verb/noun | to add to or fill in what is missing

HSK 5 | adjective | different from what is normal; exceptional; having unique qualities

HSK 5 | noun/verb/adjective | the feeling of sorrow over something missed or lost

ずっと (ずっと / zutto): all along, continuously. N4 level Japanese vocabulary.

HSK 3 | verb | to take a photo, to shine on, to reflect, to look after

Master the critical distinction between 〜かねる (polite refusal/impossibility) and 〜かねない (risk/negative possibility warning).

HSK 4 | verb | disrupting someone's activity or peace

HSK 4 | verb | holding something valuable as one's own

HSK 3 | verb / adjective | to be moved emotionally, touched deeply by something

HSK 5 | noun/adjective | green (colour); eco-friendly, sustainable, clean

The sequence in this problem comes from counting lattice points inside a growing hexagon on a hexagonal grid. Instead of having to construct the hexagon or count points manually, the problem already gives the formula for the sequence: $$Hn = 3 cdot n cdot (n+1) + 1$$ The input…

HSK 3 | adjective/expression | feeling embarrassed, shy, or apologetic; sorry to bother you

Inferring subtext, reading prosody, and decoding implicature in advanced Chinese spoken discourse — 弦外之音 and the pragmatics of indirect communication

週 (shuu/): week. JLPT N5 kanji.

HSK 1 | pronoun | interrogative pronoun asking about things or identity

HSK 4 | verb | to have capacity for a number of people or things

We are asked to maximize the minimum height of flowers after a limited number of days of watering. Each flower has an initial height, and on any day we can water a contiguous segment of exactly w flowers, increasing each by one.

HSK 3 | noun | actor, actress, performer

HSK 7 vocabulary reference: advanced C2-level words across specialized professional, academic, and literary domains.

HSK 5 | verb/noun | the operation and management of a business or service

We have all lattice points inside a rectangle of size $n times m$. Any square whose four vertices are lattice points is allowed, even if it is rotated. For every such square, we look at the unit grid cells completely contained inside it. Each contained unit cell receives one dot.

Dreamoon wants to reach the top of a staircase containing n steps. Every move can cover either 1 step or 2 steps. Among all possible ways to reach exactly step n, we need the number of moves used to be divisible by m. The task is not asking for the number of different sequences.

HSK 5 | verb | to reveal; to bring to light; to expose

HSK 3 | verb/noun | to make a journey to another place