# What are some fun math problems with integer answers from 0-18?

August 30, 2007 5:51 AM Subscribe

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.

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.

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.

Of course, there will be a cheat sheet for the drunk and/or cranky.

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.

Thanks for your help!

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.

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.

Of course, there will be a cheat sheet for the drunk and/or cranky.

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.

Thanks for your help!

how about some easy simultaneous equations, like

x +2y = 13

2x -y = 1

Solve for x

posted by electroboy at 6:03 AM on August 30, 2007

x +2y = 13

2x -y = 1

Solve for x

posted by electroboy at 6:03 AM on August 30, 2007

The alarmingly thorough Wikipedia inevitably has a page for each integer. Here's a dissertation on 3.

posted by futility closet at 6:16 AM on August 30, 2007

posted by futility closet at 6:16 AM on August 30, 2007

along the lines of what electroboy is saying, maybe a few simple trinomial factoring problems? You know, like

x^2 + 8x + 16 = 0

(x-4)^2 = 0

x = 4

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.

And also - wickedly cool idea, seriously. :D

posted by Phire at 6:18 AM on August 30, 2007

x^2 + 8x + 16 = 0

(x-4)^2 = 0

x = 4

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.

And also - wickedly cool idea, seriously. :D

posted by Phire at 6:18 AM on August 30, 2007

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.

posted by notsnot at 6:37 AM on August 30, 2007

posted by notsnot at 6:37 AM on August 30, 2007

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)?

And any crashers should be told they are seated at the square root of -1.

posted by stevis23 at 6:43 AM on August 30, 2007 [1 favorite]

And any crashers should be told they are seated at the square root of -1.

posted by stevis23 at 6:43 AM on August 30, 2007 [1 favorite]

discrete logarithms modulo 18

posted by chunking express at 6:44 AM on August 30, 2007

posted by chunking express at 6:44 AM on August 30, 2007

The rec.puzzles archive 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.

posted by edd at 6:44 AM on August 30, 2007

posted by edd at 6:44 AM on August 30, 2007

Response by poster: 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.

posted by Alison at 6:50 AM on August 30, 2007

posted by Alison at 6:50 AM on August 30, 2007

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.

posted by monkeymadness at 7:02 AM on August 30, 2007

posted by monkeymadness at 7:02 AM on August 30, 2007

A good "dammit, I can't believe I didn't see that quicker" problem, from a Martin Gardner book:

In this diagram, what is X?

posted by equalpants at 7:05 AM on August 30, 2007 [2 favorites]

In this diagram, what is X?

posted by equalpants at 7:05 AM on August 30, 2007 [2 favorites]

Lazy way out, but take any problem with an integer solution and ask for the remainder upon division by 19.

posted by parudox at 7:09 AM on August 30, 2007

posted by parudox at 7:09 AM on August 30, 2007

Figuring out how many fingers aliens have based on how they do math.

Searching for number +brainteasers brings up a bunch of questions that seem potentially useful. This page has some sequence problems at the bottom that might work.

posted by lullabyofbirdland at 7:14 AM on August 30, 2007

Searching for number +brainteasers brings up a bunch of questions that seem potentially useful. This page has some sequence problems at the bottom that might work.

posted by lullabyofbirdland at 7:14 AM on August 30, 2007

For the more math oriented, you could do something fun with e^ (i*pi) = -1.

posted by smackfu at 7:24 AM on August 30, 2007

posted by smackfu at 7:24 AM on August 30, 2007

Negative integers are fine. That's what absolute value is for. So, for example, smackfu's suggestion might be:

| e^(pi*i) |

Especially for the computer scientists, you might seriously think about loops or recursion.

Also, functions like ipart, fpart, etc. might be fun.

So, perhaps you could do:

ipart(10*[fpart(pi*10^3)]) = ?

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.

posted by JMOZ at 7:39 AM on August 30, 2007

| e^(pi*i) |

Especially for the computer scientists, you might seriously think about loops or recursion.

Also, functions like ipart, fpart, etc. might be fun.

So, perhaps you could do:

ipart(10*[fpart(pi*10^3)]) = ?

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.

posted by JMOZ at 7:39 AM on August 30, 2007

*You could do variants on the "how old is Alice" questions*

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.

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?"

posted by Rock Steady at 7:49 AM on August 30, 2007

*Also, functions like ipart, fpart, etc. might be fun.*

Heh, or casts. (int) pi * (int) e = 6

posted by smackfu at 8:04 AM on August 30, 2007

The Penguin Dictionary of Curious and Interesting Numbers 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 :)

posted by themel at 8:18 AM on August 30, 2007

posted by themel at 8:18 AM on August 30, 2007

For the computer scientists, work in different base systems, like binary and hexadecimal.

posted by rocket88 at 8:27 AM on August 30, 2007

posted by rocket88 at 8:27 AM on August 30, 2007

CAUTION: SEVERE TIME-SINK ALERT: The ever-amusing webcomic xkcd has forums, where a bunch of mathematics and logic puzzle dorks hang out. Probably more complicated than you're looking for, but perhaps worth a look for the "difficulty: evil" set...

posted by Myself at 8:31 AM on August 30, 2007

posted by Myself at 8:31 AM on August 30, 2007

The smallest right triangle am I (integral sides, area = 6).

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.)

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).

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 enough for chaos.)

posted by jamjam at 9:52 AM on August 30, 2007

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.)

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).

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 enough for chaos.)

posted by jamjam at 9:52 AM on August 30, 2007

If there really is a table of computer scientists, something involving a bit shift?

posted by juv3nal at 11:35 AM on August 30, 2007

posted by juv3nal at 11:35 AM on August 30, 2007

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.

Other fields (pun unintentional) that can produce small integer answers:

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.

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?"

It would probably be cruel to give one guest a famously unsolved problem and see what happens.

posted by hattifattener at 12:21 PM on August 30, 2007

Other fields (pun unintentional) that can produce small integer answers:

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.

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?"

It would probably be cruel to give one guest a famously unsolved problem and see what happens.

posted by hattifattener at 12:21 PM on August 30, 2007

This thread is closed to new comments.

posted by MtDewd at 5:57 AM on August 30, 2007