## Search found 43 matches

Wed Aug 01, 2007 6:32 pm UTC
Forum: Mathematics
Topic: Strange math thought (grid related)
Replies: 21
Views: 3534
Yes, in theory they're the same distance. However, this is being used for a board game. We assume, then, that this would be printed and used for playing a game on a flat surface, in which case we'd be using Euclidean distances. Why would you use Euclidean distances in a board game? Ever played Risk?
Mon Jul 23, 2007 3:47 pm UTC
Forum: Forum Games
Topic: Innuendo!
Replies: 58
Views: 10970
My tape measure isn't stiff enough ... could you grab the end for me?

beret
Tue Jun 26, 2007 10:13 pm UTC
Forum: Mathematics
Topic: What do you make of this guy?
Replies: 14
Views: 3750
Corollary: there are no Pythagorean triples.

Proof: follow the author's proof of FLT but take m=2.
Tue Jun 26, 2007 4:07 pm UTC
Forum: Mathematics
Topic: What do you make of this guy?
Replies: 14
Views: 3750
The "proof" of Goldbach's conjecture is hilarious throughout. This is a joke, right? Seriously, no one could possibly believe they have solved all these huge problems so easily. Haha, the "proof" of GC takes a whole three sentences. From what I understand of the proof, the autho...
Fri Jun 22, 2007 9:52 pm UTC
Forum: Logic Puzzles
Topic: I dare you to solve this.
Replies: 82
Views: 36113
http://www.drunkmenworkhere.org/129 As most people already figured out, this is generally unsolvable. I can't rigorously prove that it never has a feasible solution, but I ran a few of the matrices through an assignment problem solver, and for a given matrix, any choice will yield the exact same nu...
Wed Jun 20, 2007 12:50 pm UTC
Forum: Logic Puzzles
Topic: Three gods - True, False and Random
Replies: 65
Views: 36001

### Re: Three gods - True, False and Random

What a terrible curse, to be all-knowing but compelled to spit out random answers ... I bet the Ancient Greeks thought of this one.
Tue Jun 19, 2007 4:21 am UTC
Forum: Mathematics
Topic: Medians, Altitudes, and things
Replies: 8
Views: 2737
Ceva's Theorem is a good place to start.
Sun Jun 10, 2007 10:23 pm UTC
Forum: Logic Puzzles
Topic: Expected area of triangle constructed in semicircle
Replies: 13
Views: 4170
I agree with your answer. There are three cases: both P and Q are on the semicircle; one is on the circle and one on the diameter; or both are on the diameter. Suppose both P and Q are on the semicircle. Let alpha and beta be the angles subtended along the semicircle to P and Q, respectively; assum...
Sun May 13, 2007 1:27 pm UTC
Forum: Mathematics
Replies: 139
Views: 24504
Best calculator I've ever had is my Radio Shack EC-4032. My dad bought it for me for high school 13 years ago, and I've used it ever since. I had a TI-83 at one point, but it just wasn't the same. This calculator kept me sane through the tedium of high school math: it helped me learn bases other tha...
Tue May 08, 2007 3:48 am UTC
Forum: Mathematics
Topic: Division Induction
Replies: 16
Views: 9198
How about this: n^3 + 5n is divisible by 6 if and only if n^3 - n is divisible by 6. This latter polynomial is the product of three consecutive numbers: (n-1)(n)(n+1), one of which obviously must be even, and one of which must be a multiple of 3. Edit: yes, I know it's not induction. Sometimes you j...
Tue May 08, 2007 3:45 am UTC
Forum: Mathematics
Topic: Multiplication of a number in a non-10 base?
Replies: 26
Views: 11628
If you choose base n, where n-1 has many factors, then you get a lot of easy divisibility tests for free: let d be a factor of n-1; then x is a multiple of d if and only if the digits of x add up to a multiple of d. e.g. in the ever-so-convenient base 92, you can quickly see that 3TD1DZDDD7 is a mul...
Mon May 07, 2007 11:32 pm UTC
Forum: Logic Puzzles
Topic: 4=5[solution]
Replies: 52
Views: 9203
I'm not sure if this has been resolved yet (I skipped a page of arguing), but for those who need a non-Wikipedic reference to truly believe that sqrt(x) refers to the positive square root of x, consider "A Course in Pure Mathematics" by G.H. Hardy. Irrational numbers are dealt with in the ...
Sat May 05, 2007 6:43 pm UTC
Forum: Mathematics
Topic: n and n-1
Replies: 6
Views: 4523

### Re: n and n-1

3.14159265... wrote:edit: Also, the full factorization of n-1 would also be nice ...

It sure would be nice. That would let you factorise any number n extremely quickly: just choose a prime p bigger than n, then magically compute the full factorisations of p-1, p-2, ..., until you get to n.
Sat May 05, 2007 6:39 pm UTC
Forum: Mathematics
Topic: How many digits of Pi do you know?
Replies: 445
Views: 108412
Back in high school I had about 256 digits memorised (I had painted the first 170 or so around my room), but I'm getting old and losing my memory ... let's see ... 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480806647093844609 and now I'm ...
Tue May 01, 2007 2:35 pm UTC
Forum: Logic Puzzles
Topic: Checkmate with one piece
Replies: 4
Views: 2746
I don't understand: if black can't move, then what distinguishes check from checkmate?
Sun Apr 29, 2007 5:43 pm UTC
Forum: Logic Puzzles
Topic: Unusual Paragraph
Replies: 36
Views: 9029
Indeed. Fynch, if you're going to be nitpicky, it helps if (a) there's a point, and (b) you quote your source in a standard and intelligible way. I must confess that I had no clue what you were talking about (I wondered if it was a new puzzle in the same vein as the one starting this thread) until R...
Sat Apr 28, 2007 2:12 pm UTC
Forum: Logic Puzzles
Topic: Unusual Paragraph
Replies: 36
Views: 9029
The amazing thing is, someone once wrote an entire book in French with that same trick. Even more amazing, it got translated to English, again using the same trick. I think the original French ("La Disparation" by Georges Perec) is much more amazing than the fact that it was translated in...
Fri Apr 27, 2007 4:11 pm UTC
Forum: Logic Puzzles
Topic: A field of theorems
Replies: 12
Views: 3186
I used to think about this sort of thing in graph theory classes (and I think graphs provide a much more natural and feasible structure than do fields ...). Let G be a graph with vertices (side note: Firefox spelling helper knows 'vertexes' but not 'vertices'? shame!) labelled according to graph-the...
Mon Mar 19, 2007 3:20 pm UTC
Forum: Logic Puzzles
Topic: Lowest price auctions PUZZLE
Replies: 58
Views: 14931
Token wrote:
MMoto wrote:These aren't Nash equilibria, since every player would want to switch to n+1 to become the winner.

That wouldn't work, since as soon as they switch, the other player with their original number now has the lowest unique number.

Sun Mar 18, 2007 3:19 pm UTC
Forum: Logic Puzzles
Topic: Lowest price auctions PUZZLE
Replies: 58
Views: 14931
skeptical scientist wrote:If there are 4 players, then 2 players playing 1, and 2 players playing 2 is a Nash equilibrium. Similarly, for 2n players, 2 players each playing 1, 2, ..., n is a Nash equilibrium.

These aren't Nash equilibria, since every player would want to switch to n+1 to become the winner.
Sat Mar 17, 2007 6:11 am UTC
Forum: Logic Puzzles
Topic: Lowest price auctions PUZZLE
Replies: 58
Views: 14931
Alky wrote:I haven't actually done the calculations, but this is my instinct. It clearly works for the 2-person case (you expect to win half the time).

In the 2-person case, suppose your opponent always picks 1.
Then you lose half the time and draw half the time.
Fri Feb 16, 2007 6:30 pm UTC
Forum: Forum Games
Topic: 3 letters in a word
Replies: 1802
Views: 284996
Zamboni.

oau
Wed Feb 07, 2007 8:16 pm UTC
Forum: Logic Puzzles
Topic: Fornicating Chesspeople
Replies: 20
Views: 6451
For anyone interested in taking this further, these objects are called "dynamos" in the literature.
Mon Jan 29, 2007 4:55 am UTC
Forum: Logic Puzzles
Topic: Riddle I Came Up With- No Maths Required!
Replies: 29
Views: 8405
I'd guess bread, but I don't know if the usefulness of bread can be quantified.
Sat Jan 20, 2007 1:36 am UTC
Forum: Forum Games
Topic: 3 letters in a word
Replies: 1802
Views: 284996
Pterodactyl.

You gave 3/3 of a word earlier, Skeptical Scientist (ghi) ... :)

ioi
Sat Dec 16, 2006 8:47 am UTC
Forum: Logic Puzzles
Topic: The Man Who Shot Liberty Valance - [solutions]
Replies: 15
Views: 5964
If the sun is hot enough to melt a jar, then it might not matter anyway ... !

Sat Dec 16, 2006 8:16 am UTC
Forum: Logic Puzzles
Topic: The Man Who Shot Liberty Valance - [solutions]
Replies: 15
Views: 5964
My solution, assuming that the jar is a standard shape:

Wayne pours half the water into the cup, then passes the cup to Marvin. The jar is half-empty when the jar can be tilted so that the plane of the water surface is tangent to both the bottom and the top of the jar.
Sat Dec 16, 2006 2:40 am UTC
Forum: Logic Puzzles
Topic: The Man Who Shot Liberty Valance - [solutions]
Replies: 15
Views: 5964

### The Man Who Shot Liberty Valance - [solutions]

Nicely-worded problem. :)

I get A, B, C all possible, using the same method for each.

Edit: removed annoying white text.
Wed Dec 13, 2006 8:03 pm UTC
Forum: Logic Puzzles
Topic: Hand-Shaking
Replies: 8
Views: 4835
I shook hands with him
I have shaken the ketchup.

It's like the Elvis song, "I'm all shaken up".
Tue Dec 12, 2006 3:39 am UTC
Forum: Logic Puzzles
Replies: 6
Views: 3094
flatluigi wrote:Sorry about that. I meant 9 to 5 players.

Ah, right, I was going to write that as a fifth option but forgot. I think this was confusing because you'd typically write 5 to 9 players, not 9 to 5. Anyway...
Tue Dec 12, 2006 2:26 am UTC
Forum: Logic Puzzles
Replies: 6
Views: 3094

You have 9 kids definitely on your team. For 9-5 players, create a plan for playing time. Try to make the schedules with that ability. Just to clarify: what do you mean by 9-5 players? (a) 9-5 = 4 (b) Kids who play daytime basketball (9:00 AM - 5:00 PM) (c) There are nine kids on the team, and 5 pl...
Thu Dec 07, 2006 7:22 am UTC
Forum: Logic Puzzles
Topic: Unfair Beans [Solution]
Replies: 1
Views: 1997
Very nicely written! Indeed that is the solution.
Mon Dec 04, 2006 7:30 am UTC
Forum: Logic Puzzles
Topic: Temperatures
Replies: 60
Views: 13454
By the way, you actually can multiply ordinal numbers. For example, second times third is six thth . But they aren't a distinct group from decimals. They're pretty much the same. *ahem* Please note humour in original post. Anyway, Twasbrillig, I don't know what your background is, but it sounds lik...
Mon Dec 04, 2006 4:06 am UTC
Forum: Logic Puzzles
Topic: Temperatures
Replies: 60
Views: 13454
By the way, you actually can multiply ordinal numbers. For example, second times third is sixthth.
Mon Dec 04, 2006 2:51 am UTC
Forum: Logic Puzzles
Topic: Temperatures
Replies: 60
Views: 13454
The ancient Babylonians did not have negative numbers or infinity. Therefore they did not multiply. And that's why they're not around any more. Exactly. They didn't have those, so they couldn't logically multiply, because they didn't have a numerical scale. Since temperatures are measured with sequ...
Mon Dec 04, 2006 12:35 am UTC
Forum: Logic Puzzles
Topic: Unfair beans
Replies: 7
Views: 3773

### Re: Unfair beans

I think there might be some confusion about the number of piles. There are n piles , with sizes 1, 2, 3, ..., n . For which n does Player 2 have a guaranteed win regardless of who goes first? Note that there are n piles, ranging in size from 1 to n , as opposed to a single pile with n beans. For n =...
Mon Dec 04, 2006 12:10 am UTC
Forum: Logic Puzzles
Topic: Unfair beans
Replies: 7
Views: 3773
n=3x-1. Any multiple of three, minus one. 2, 5, 8, 11, etc. I'm not sure why yet. I'll figure it out and get back to you. Player 2 doesn't have a guaranteed win for n = 2. If Player 1 goes first, he removes one bean from the larger pile, leaving two 1-bean piles. Player 2 will lose.
Sun Dec 03, 2006 10:58 pm UTC
Forum: Logic Puzzles
Topic: Unfair beans
Replies: 7
Views: 3773

### Unfair beans

In keeping with the bean theme, here's something that I came up with today. As usual, two players take turns removing beans from piles; whoever takes the last bean wins. For this game, Player 1 can only remove one bean at a time, while Player 2 can only remove two beans at a time, or remove the sing...
Sun Dec 03, 2006 6:48 pm UTC
Forum: Logic Puzzles
Topic: Temperatures
Replies: 60
Views: 13454
The ancient Babylonians did not have negative numbers or infinity.
Therefore they did not multiply. And that's why they're not around any more.
Sun Dec 03, 2006 3:34 am UTC
Forum: Logic Puzzles
Topic: More beans
Replies: 11
Views: 4173
Hmmm. I don't see how this can have a closed-form solution. Let P be the set of numbers one less than prime, i.e. P = {1, 2, 4, 6, ...}. Let W1 be the set of first-player wins, and W2 the set of second-player wins. Then W1 and W2 are the (unique) sets that satisfy the following: ⋅ * for al...