Credits

Lesson order, grammar points and vocabulary for the Minna no Nihongo units follow this textbook. Explanations, examples and exercises are written for Learnr.

Topic and grammar order for this course follows this free DW course. Explanations, dialogues and exercises are written for Learnr.

Reference for place value, expanded form, number lines and rounding. Our examples and exercises are original.

Mathematical background for rearranging and regrouping sums and products. QuantArc derives its mental calculation routes from these identities.

Free textbook reference for distributing and regrouping. QuantArc's explanations and exercises are original.

Author-hosted paper, pp. 58-59, on choosing a nearby easy base. Our square shortcuts are algebraic special cases, not copied book lessons.

Explains the consecutive-number product and its algebraic proof, including numbers longer than two digits.

Free course site with videos and the open companion book Introduction to Probability; the topic spine for counting, Bayes, and linearity. Lesson examples and questions are original.

Free step-by-step walkthroughs of classic probability interview puzzles by difficulty; companion practice. Lesson examples and questions are original.

Supports worked examples, retrieval, explanations and spaced study. Does not establish QuantArc's exact lesson length, mastery threshold or review intervals.

Recommended reading. Publisher description checked; full book text has not been verified against these lessons.

Publisher description checked only; further reading on multiplication and division. The full chapter methods have not been verified against these lessons. Lesson examples are original.

Reference-number multiplication and division-by-factors chapters (table of contents seen only; recommended further reading; lesson examples are original).

Contents-level reference for division and shortcut arithmetic; further reading only. Full worked examples and decimal-divisor methods have not been reviewed against these lessons. Lesson examples are original.

Lecture titles and synopses seen only, including intermediate multiplication with the close-together method; recommended further reading; lesson examples are original.

Chapter VI on fractions, mixed numbers, and percentages (contents page seen). Lesson examples are original.

Lecture 4 synopsis names division shortcuts including 1/7 and 3/16 conversion (synopses seen only; recommended further reading; lesson examples are original).

Library descriptions confirm break-apart addition and drill structure (full chapter text not read; recommended further reading; lesson examples are original).

Chapter 5 guesstimation (chapter list seen; recommended further reading; lesson examples are original).

Lecture 5 synopsis seen only (estimation of all four operations plus square roots; recommended further reading; lesson examples are original).

Indexed-text terms seen only (casting out nines, digit-sum check); recommended further reading; lesson examples are original.

Indexed-text terms seen only (nines-remainders, elevens-remainder, digit sums); recommended further reading; lesson examples are original.

Series chapter (arithmetic, geometric, mixed) at chapter-title level only (contents listing seen); recommended further reading; lesson examples are original.

Decision-theoretic analysis of formula scoring and rational guessing after eliminating distractors. Lesson examples and numbers are original.

Bibliographic reference for interview preparation; the library catalogue identifies the book, but does not verify its chapter methods or these lessons' fair-value and odds claims. Full book text has not been reviewed. Lesson examples and questions are original.

Foundational paper for the Kelly criterion optimizing compound wealth growth. Lesson framing and calculations are original.

Discussion of full vs fractional Kelly, parameter uncertainty, and drawdown risk. Lesson examples and questions are original.

Landing page checked: Jane Street's card game that simulates elements of markets and trading, with rules, a tutorial and a learning mode. Practice companion only; its rules and strategy tips were not reviewed against these lessons. Lesson examples are original.

Official rules page fetched and checked: 40-card deck with two 10-card suits, one 8-card suit and one 12-card suit; goal suit shares the 12-card suit color and holds 8 or 10 cards; $200 pot with $10 per goal card and the rest to the most goal cards. Lesson examples are original.

Listing page checked: browser games including market making on dice, a card market-taking game, Fermi estimation and a trading game. Practice companion only; game content was not played or reviewed against these lessons. Lesson examples are original.

Interview preparation guide (page 9) testing optimal stopping and market making on a d6 with one optional reroll. Lesson examples and questions are original.

Official Options Clearing Corporation disclosure document outlining standardized option contract specifications, exercise settlement, payoff obligations, and intrinsic value mechanics.

Recommended textbook reference. Publisher overview and table of contents checked for option properties, binomial trees, Black-Scholes-Merton and Greeks; full derivations and exercises have not been audited against these lessons. Lesson examples and exercises are original.

Educational curriculum on option payoff curves, long straddle breakevens, synthetic positions, and market volatility characteristics.

Course page checked: undergraduate discrete mathematics covering permutations and combinations plus counting principles. Topic spine for stars and bars, lattice paths, and derangements. Lesson examples and questions are original.

Free textbook PDF confirmed live: counting methods, poker-style dealing models, and the random-walk chapter behind gambler's ruin and first-step equations. Lesson examples and questions are original.

MIT archive record checked: Muhamet Yildiz's Fall 2012 course introduces game-theoretic analysis and economic applications. The original OCW page is retired; the archive offers a course ZIP. Archive contents have not been reviewed here, so this record does not verify the lessons' specific auction or equilibrium claims. Lesson examples and questions are original.

Course page checked: auction formats, Vickrey dominance, Bayes-Nash bidding with uniform values, common-value winner curse intuition, and zero-sum mixed equilibria. Lesson examples and questions are original.

Firm page checked: decision science culture with poker, strategy games, and bias case studies. Motivation companion for the game theory track. Lesson examples and questions are original.

Fetched problem collection seen: estimation prompts including the piano-tuner question, with stated assumptions and unit chains. Lesson examples and questions are original.

Static emoji artwork.

Animated emoji artwork, self-hosted.

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Body typeface.