Divisibility Rules for Numbers 1 through 20 — Presented by Calculus Humor 
A divisibility rule is a shorthand way of determining whether a given number is divisible by a fixed divisor without performing the division, usually by examining its digits. Below are divisibility rules for numbers 1 through 20. This chart and printable guide were compiled and prepared by Gregory Tewksbury, a cofounder of Calculus Humor! Attached is a printable pdf handout (fits on the front of a single 8½ by 11 inch or lettersized sheet of paper) of these rules, which makes it a great classroom or personal aid! Feel free to use for personal use or classroom use only!
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We posted "How to Prove It: Guide for Lecturers" way back in August. Now it is time to revisit it and play "How to Prove It: Guide for Lecturers Bingo!" How to play: Before each math class, visit How to Prove It: Guide for Lecturers Bingo and print one copy of this game card for each player, refreshing the page before each print, or have the players print their own bingo cards. These instructions will not be printed. You can also select card only and multiple card versions of this page when playing online, or with a PDA. Check off each block when you hear these words during the class. When you get five blocks horizontally, vertically, or diagonally, stand up and shout "EUREKA!!!". Need to refresh what the definitions are? Then visit http://www.calculushumor.com/3/post/2012/08/howtoproveitguideforlecturers.html.
A divisibility rule is a shorthand way of determining whether a given number is divisible by a fixed divisor without performing the division, usually by examining its digits. Below are divisibility rules for numbers 1 through 20. This chart and printable guide were compiled and prepared by Gregory Tewksbury, a cofounder of Calculus Humor! Attached is also a printable pdf of these rules! Feel free to use for personal use or classroom use only!
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Proof by vigorous handwaving: Works well in a classroom or seminar setting.
Proof by forward reference: Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first. Proof by funding: How could three different government agencies be wrong? Proof by example: The author gives only the case n = 2 and suggests that it contains most of the ideas of the general proof. Proof by omission: "The reader may easily supply the details" or "The other 253 cases are analogous" Proof by deferral: "We'll prove this later in the course". Proof by picture: A more convincing form of proof by example. Combines well with proof by omission. Proof by intimidation: "Trivial." Proof by adverb: "As is quite clear, the elementary aforementioned statement is obviously valid." Proof by seduction: "Convince yourself that this is true! " Proof by cumbersome notation: Best done with access to at least four alphabets and special symbols. Proof by exhaustion: An issue or two of a journal devoted to your proof is useful. Proof by obfuscation: A long plotless sequence of true and/or meaningless syntactically related statements. Proof by wishful citation: The author cites the negation, converse, or generalization of a theorem from the literature to support his claims. Proof by eminent authority: "I saw Karp in the elevator and he said it was probably NP complete." Proof by personal communication: "Eightdimensional colored cycle stripping is NPcomplete [Karp, personal communication]." Proof by reduction to the wrong problem: "To see that infinitedimensional colored cycle stripping is decidable, we reduce it to the halting problem." Proof by reference to inaccessible literature: The author cites a simple corollary of a theorem to be found in a privately circulated memoir of the Slovenian Philological Society, 1883. Proof by importance: A large body of useful consequences all follow from the proposition in question. Proof by accumulated evidence: Long and diligent search has not revealed a counterexample. Proof by cosmology: The negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of God. Proof by mutual reference: In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown to follow from Corollary 6.2 in reference C, which is an easy consequence of Theorem 5 in reference A. Proof by metaproof: A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques. Proof by vehement assertion: It is useful to have some kind of authority relation to the audience. Proof by ghost reference: Nothing even remotely resembling the cited theorem appears in the reference given. Proof by semantic shift: Some of the standard but inconvenient definitions are changed for the statement of the result. Proof by appeal to intuition: Cloudshaped drawings frequently help here. CLEARLY:
I don't want to write down all the "in between" steps. TRIVIAL: If I have to show you how to do this, you're in the wrong class. OBVIOUSLY: I hope you weren't sleeping when we discussed this earlier, because I refuse to repeat it. RECALL: I shouldn't have to tell you this, but for those of you who erase your memory tapes after every test... WLOG (Without Loss Of Generality): I'm not about to do all the possible cases, so I'll do one and let you figure out the rest. CHECK or CHECK FOR YOURSELF: This is the boring part of the proof, so you can do it on your own time. SKETCH OF A PROOF: I couldn't verify all the details, so I'll break it down into the parts I couldn't prove. HINT: The hardest of several possible ways to do a proof. SOFT PROOF: One third less filling (of the page) than your regular proof, but it requires two extra years of course work just to understand the terms. ELEGANT PROOF: Requires no previous knowledge of the subject matter and is less than ten lines long. SIMILARLY: At least one line of the proof of this case is the same as before. CANONICAL FORM: 4 out of 5 mathematicians surveyed recommended this as the final form for their students who choose to finish. BY A PREVIOUS THEOREM: I don't remember how it goes (come to think of it I'm not really sure we did this at all), but if I stated it right (or at all), then the rest of this follows. TWO LINE PROOF: I'll leave out everything but the conclusion, you can't question 'em if you can't see 'em. BRIEFLY: I'm running out of time, so I'll just write and talk faster. LET'S TALK THROUGH IT: I don't want to write it on the board lest I make a mistake. PROCEED FORMALLY: Manipulate symbols by the rules without any hint of their true meaning (popular in pure math courses). QUANTIFY: I can't find anything wrong with your proof except that it won't work if x is a moon of Jupiter. PROOF OMITTED: Trust me, It's true. 
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