Comments on: What are some fun math problems with integer answers from 0-18?

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

Alison — Thu, 30 Aug 2007 05:51:45 -0800

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!

By: MtDewd

MtDewd — Thu, 30 Aug 2007 05:57:17 -0800

This calculus sudoku has a bunch to choose from for 1-9.

By: electroboy

electroboy — Thu, 30 Aug 2007 06:03:13 -0800

how about some easy simultaneous equations, like

x +2y = 13
2x -y = 1

Solve for x

By: futility closet

futility closet — Thu, 30 Aug 2007 06:16:30 -0800

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

By: Phire

Phire — Thu, 30 Aug 2007 06:18:37 -0800

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

By: notsnot

notsnot — Thu, 30 Aug 2007 06:37:51 -0800

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.

By: stevis23

stevis23 — Thu, 30 Aug 2007 06:43:17 -0800

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.

By: chunking express

chunking express — Thu, 30 Aug 2007 06:44:28 -0800

discrete logarithms modulo 18

By: edd

edd — Thu, 30 Aug 2007 06:44:35 -0800

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.

By: Alison

Alison — Thu, 30 Aug 2007 06:50:01 -0800

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.

By: monkeymadness

monkeymadness — Thu, 30 Aug 2007 07:02:26 -0800

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.

By: equalpants

equalpants — Thu, 30 Aug 2007 07:05:23 -0800

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?

By: parudox

parudox — Thu, 30 Aug 2007 07:09:20 -0800

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

By: phatkitten

phatkitten — Thu, 30 Aug 2007 07:10:07 -0800

Solve for the hypotenuse on a right triangle?

By: lullabyofbirdland

lullabyofbirdland — Thu, 30 Aug 2007 07:14:42 -0800

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.

By: smackfu

smackfu — Thu, 30 Aug 2007 07:24:13 -0800

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

By: JMOZ

JMOZ — Thu, 30 Aug 2007 07:39:59 -0800

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.

By: Rock Steady

Rock Steady — Thu, 30 Aug 2007 07:49:09 -0800

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?"

By: smackfu

smackfu — Thu, 30 Aug 2007 08:04:28 -0800

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

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

By: themel

themel — Thu, 30 Aug 2007 08:18:03 -0800

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 :)

By: rocket88

rocket88 — Thu, 30 Aug 2007 08:27:30 -0800

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

By: Myself

Myself — Thu, 30 Aug 2007 08:31:54 -0800

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...

By: dfan

dfan — Thu, 30 Aug 2007 09:32:24 -0800

Why was 6 afraid of 7?

By: jamjam

jamjam — Thu, 30 Aug 2007 09:52:20 -0800

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.)

By: juv3nal

juv3nal — Thu, 30 Aug 2007 11:35:04 -0800

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

By: hattifattener

hattifattener — Thu, 30 Aug 2007 12:21:34 -0800

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.