Comments on: What are some fun math problems with integer answers from 0-18?
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018/
Comments on Ask MetaFilter post What are some fun math problems with integer answers from 0-18?Thu, 30 Aug 2007 05:57:17 -0800Thu, 30 Aug 2007 05:57:17 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Question: What are some fun math problems with integer answers from 0-18?
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018
What are some (easy to moderate difficulty) math problems with integer answers ranging from 0-18? I'm making mathematical seating cards where guests will solve a problem to find their table number. <br /><br /> Ideally, the problems could be solved quickly without pen and paper and fit on half of a business card sized piece of card stock. Each table will have the same card for all of its guests so that they can be compared to make sure that each guest is in the right place. Our favorite problems have a visual element to them, like a diagram or a picture. Also, positive integers only, please! Though I know it is tempting to make people sit at table pi, we made the table numbers last week and don't want to make them again.<br>
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Our guests run the gamut of math skills, so the difficulty level will be different based on the table. For example, the table full of computer scientists will get a much different problem than the print artist table. Our table assignments aren't set in stone yet, so multiple problems per table number would be great.<br>
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Of course, there will be a cheat sheet for the drunk and/or cranky.<br>
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I have a few problems already (the slope of a horizontal line for table zero, a problem with Japanese numerals for my anime-loving cousins, etc.), but I'm sure that there are much more creative and math-savvy people on this site than me.<br>
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Thanks for your help!post:ask.metafilter.com,2007:site.70445Thu, 30 Aug 2007 05:51:45 -0800AlisonmathweddingpuzzleseatingcardBy: MtDewd
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050833
This <a href="http://homework.zendog.org/xmassudoku.pdf">calculus sudoku</a> has a bunch to choose from for 1-9.comment:ask.metafilter.com,2007:site.70445-1050833Thu, 30 Aug 2007 05:57:17 -0800MtDewdBy: electroboy
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050839
how about some easy simultaneous equations, like<br>
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x +2y = 13<br>
2x -y = 1<br>
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Solve for xcomment:ask.metafilter.com,2007:site.70445-1050839Thu, 30 Aug 2007 06:03:13 -0800electroboyBy: futility closet
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050844
The alarmingly thorough Wikipedia inevitably has a page for each integer. Here's <a href="http://en.wikipedia.org/wiki/3_%28number%29">a dissertation on 3</a>.comment:ask.metafilter.com,2007:site.70445-1050844Thu, 30 Aug 2007 06:16:30 -0800futility closetBy: Phire
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050846
along the lines of what electroboy is saying, maybe a few simple trinomial factoring problems? You know, like <br>
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x^2 + 8x + 16 = 0<br>
(x-4)^2 = 0<br>
x = 4<br>
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Of course, they would have to be perfect square trinomials. Unless you wanted to add an extra step of "since x must be a positive integer, answer #1 is inadmissible, therefore x must be..." etc. <br>
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And also - wickedly cool idea, seriously. :Dcomment:ask.metafilter.com,2007:site.70445-1050846Thu, 30 Aug 2007 06:18:37 -0800PhireBy: notsnot
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050861
There's a Math calendar by Theoni Pappas puts out each year, with the answers to each day's puzzler being the day in question. Some problems are hella hard, some or retarded easy. All problems fit inside a typical calendar square. I could fax you some old ones for ideas.comment:ask.metafilter.com,2007:site.70445-1050861Thu, 30 Aug 2007 06:37:51 -0800notsnotBy: stevis23
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050867
You could do variants on the "how old is Alice" questions, e.g. if Alice is half of Bob's age now, how old will she be in 9 years if she is then 2/3 of Bob's age (in 9 years)?<br>
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And any crashers should be told they are seated at the square root of -1.comment:ask.metafilter.com,2007:site.70445-1050867Thu, 30 Aug 2007 06:43:17 -0800stevis23By: chunking express
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050869
discrete logarithms modulo 18comment:ask.metafilter.com,2007:site.70445-1050869Thu, 30 Aug 2007 06:44:28 -0800chunking expressBy: edd
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050870
The <a href="http://rec-puzzles.org/">rec.puzzles archive</a> is an amazing resource for problems, many of which will be entertainingly phrased and I'm sure you can find some of suitable difficulty in there.comment:ask.metafilter.com,2007:site.70445-1050870Thu, 30 Aug 2007 06:44:35 -0800eddBy: Alison
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050873
We have Theoni Pappas's calendar. Unfortunately, most of the problems are too hard to be done by the average person without pen and paper.comment:ask.metafilter.com,2007:site.70445-1050873Thu, 30 Aug 2007 06:50:01 -0800AlisonBy: monkeymadness
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050880
Combinatorics are great for coolness factor mixed with accessibility. "How many pairs can be chosen from a group of six? = 6C2 = 15" "How many ways can you color a map of three countries if you've got three colors from which to choose and no color can be used twice?" = 3! = 6.comment:ask.metafilter.com,2007:site.70445-1050880Thu, 30 Aug 2007 07:02:26 -0800monkeymadnessBy: equalpants
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050883
A good "dammit, I can't believe I didn't see that quicker" problem, from a Martin Gardner book:<br>
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In <a href="http://thinkingpart.com/tri-puzzle.png">this diagram</a>, what is X?comment:ask.metafilter.com,2007:site.70445-1050883Thu, 30 Aug 2007 07:05:23 -0800equalpantsBy: parudox
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050887
Lazy way out, but take any problem with an integer solution and ask for the remainder upon division by 19.comment:ask.metafilter.com,2007:site.70445-1050887Thu, 30 Aug 2007 07:09:20 -0800parudoxBy: phatkitten
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050890
Solve for the hypotenuse on a right triangle?comment:ask.metafilter.com,2007:site.70445-1050890Thu, 30 Aug 2007 07:10:07 -0800phatkittenBy: lullabyofbirdland
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050895
Figuring out <a href="http://mathforum.org/library/drmath/view/57148.html">how many fingers</a> aliens have based on how they do math.<br>
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Searching for number +brainteasers brings up a bunch of questions that seem potentially useful. <a href="http://brainden.com/number-puzzles.htm">This</a> page has some sequence problems at the bottom that might work.comment:ask.metafilter.com,2007:site.70445-1050895Thu, 30 Aug 2007 07:14:42 -0800lullabyofbirdlandBy: smackfu
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050903
For the more math oriented, you could do something fun with e^ (i*pi) = -1.comment:ask.metafilter.com,2007:site.70445-1050903Thu, 30 Aug 2007 07:24:13 -0800smackfuBy: JMOZ
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050926
Negative integers are fine. That's what absolute value is for. So, for example, smackfu's suggestion might be:<br>
<br>
| e^(pi*i) |<br>
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Especially for the computer scientists, you might seriously think about loops or recursion. <br>
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Also, functions like ipart, fpart, etc. might be fun.<br>
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So, perhaps you could do:<br>
ipart(10*[fpart(pi*10^3)]) = ?<br>
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For that one, you could do several of the same one (even for different tables) and just replace the 3 to use a different digit of pi.comment:ask.metafilter.com,2007:site.70445-1050926Thu, 30 Aug 2007 07:39:59 -0800JMOZBy: Rock Steady
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050946
<em>You could do variants on the "how old is Alice" questions</em><br>
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For guest-embarrassing fun, do one of those involving the real ages of some of the guests at the table, if those guests are sensitive about that sort of thing. Obviously, you don't want to piss someone off, but this sort of gag would go over well with my family/friends.<br>
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Also, to encourage mingling between groups, ask some questions that require some interviewing of unrelated people -- "How many cousins does Alison have?" or "How many degrees does Professor VonSmartypants have?" or "What is the last digit in Friendy McCollegepal's phone number?"comment:ask.metafilter.com,2007:site.70445-1050946Thu, 30 Aug 2007 07:49:09 -0800Rock SteadyBy: smackfu
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1050972
<i>Also, functions like ipart, fpart, etc. might be fun.</i><br>
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Heh, or casts. (int) pi * (int) e = 6comment:ask.metafilter.com,2007:site.70445-1050972Thu, 30 Aug 2007 08:04:28 -0800smackfuBy: themel
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1051000
<a href="http://www.amazon.com/exec/obidos/ASIN/0140261494/metafilter-20/ref=nosim/">The Penguin Dictionary of Curious and Interesting Numbers</a> has a fun microfacts you could build on. I vote for cross-referencing ("The (Alice's number)'th power of the (Bob's number)'th prime") - then, make it circular and let your guests prove they can sit anywhere they like :)comment:ask.metafilter.com,2007:site.70445-1051000Thu, 30 Aug 2007 08:18:03 -0800themelBy: rocket88
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1051016
For the computer scientists, work in different base systems, like binary and hexadecimal.comment:ask.metafilter.com,2007:site.70445-1051016Thu, 30 Aug 2007 08:27:30 -0800rocket88By: Myself
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1051024
CAUTION: SEVERE TIME-SINK ALERT: The ever-amusing webcomic <a href="http://xkcd.com/">xkcd</a> has <a href="http://forums.xkcd.com/">forums</a>, where a bunch of <a href="http://forums.xkcd.com/viewforum.php?f=17&sid=8c1fbf0b906d65038bd1c1ed6edb271c">mathematics</a> and <a href="http://forums.xkcd.com/viewforum.php?f=3&sid=8c1fbf0b906d65038bd1c1ed6edb271c">logic puzzle</a> dorks hang out. Probably more complicated than you're looking for, but perhaps worth a look for the "difficulty: evil" set...comment:ask.metafilter.com,2007:site.70445-1051024Thu, 30 Aug 2007 08:31:54 -0800MyselfBy: dfan
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1051112
Why was 6 afraid of 7?comment:ask.metafilter.com,2007:site.70445-1051112Thu, 30 Aug 2007 09:32:24 -0800dfanBy: jamjam
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1051155
The smallest right triangle am I (integral sides, area = 6).<br>
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For any number, of squares at least you must have me. (Any positive integer can be represented as the sum of at most 4 squares of other integers.)<br>
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The square of a cube and the cube of a square; I am the smallest-- divided by as many colors as National Geographic will ever need (64/4 = 16).<br>
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If chaos is your aim, equations and variables as many as I am are all that you require. (3 variables and 3 equations with some nonlinearity are <a href="http://www.its.caltech.edu/~mcc/chaos_new/Chua_docs/analysis.html">enough for chaos</a>.)comment:ask.metafilter.com,2007:site.70445-1051155Thu, 30 Aug 2007 09:52:20 -0800jamjamBy: juv3nal
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1051335
If there really is a table of computer scientists, something involving a <a href="http://en.wikipedia.org/wiki/Bitwise_operation#Bit_shifts">bit shift</a>?comment:ask.metafilter.com,2007:site.70445-1051335Thu, 30 Aug 2007 11:35:04 -0800juv3nalBy: hattifattener
http://ask.metafilter.com/70445/What-are-some-fun-math-problems-with-integer-answers-from-018#1051407
I like the idea of a problem that produces several answers — say, a set of simultaneous equations that tell you where three of the guests sit. Again this can encourage mingling and comparing-of-notes.<br>
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Other fields (pun unintentional) that can produce small integer answers:<br>
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Group theory. If you avoid terms like homeomorphism and Abelian, and phrase questions with physical examples, this could be done by guests who aren't math geeks. Extra yuks for giving two guests the exact same difficult problem in different guises.<br>
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Graph theory. "Find a hamiltonian cycle through this graph of guests and seat yourselves in that order at the table." "Which node can you delete to make this graph planar?"<br>
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It would probably be cruel to <a href="http://www.umass.edu/wsp/statistics/tales/dantzig.html">give one guest a famously unsolved problem</a> and see what happens.comment:ask.metafilter.com,2007:site.70445-1051407Thu, 30 Aug 2007 12:21:34 -0800hattifattener