Garlonuss
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Schik wrote:
The opposite of "A AND B" isn't "NOT A AND NOT B" - it's "NOT A OR NOT B".

I know and I can accept that. However, with that still in mind, my solution still seems to work out even under that constraint so, unless someone can point out a real error in my solution (which I am completely open to) it would appear that there may not be a single way to interpret this puzzle.

Never mind, I found my error.

[Edited by Garlonuss at Local Time:02-22-2005 at 10:17 PM]

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Schik
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Garlonuss wrote:

Schik wrote:
The opposite of "A AND B" isn't "NOT A AND NOT B" - it's "NOT A OR NOT B".

I know and I can accept that. However, with that still in mind, my solution still seems to work out even under that constraint so, unless someone can point out a real error in my solution (which I am completely open to) it would appear that there may not be a single way to interpret this puzzle.

Eytan says, "It's false that Mike is a Delver." In your solution, Eytan is a Smitemaster, meaning he speaks the truth. But Mike is a Delver in your solution. Contradiction.


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Maurog
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stigant wrote:
That's not the point... the condition I gave for 17 and 19 IS a positive definition (ie when you multiply their last digit by 4, you get the first two digits of their square), and 13 fails it.

I'm not arguing with that, it is correct. The point is, the numbers 1, 2 and 3 fail it too

stigant wrote:
For that matter, being prime could be (and usually IS) stated negatively: Any number that does not have divisors other than itself and 1. Whereas being composite is stated positively: HAS divisors other than itself and 1.

This is correct too. But while the primes group is a complement of the composites group and vice versa, "primes" are a known and acknowledged group mentioned countless times, including in this thread. "Non-squares" however is clearly a group defined as a complement. If you will be asked what features the number 13 has, "prime" would be among the first you will come out with, and I seriously doubt "non-square" will be mentioned at all.

That's why Schik deserves a point for answering "2 is even" even if it's not what I had in mind (people are too attached to the "odd" and "even" groups), and Hix doesn't deserve a point for answering "1 is the only square".

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Hix
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Maurog wrote:

This is correct too. But while the primes group is a complement of the composites group and vice versa, "primes" are a known and acknowledged group mentioned countless times, including in this thread. "Non-squares" however is clearly a group defined as a complement. If you will be asked what features the number 13 has, "prime" would be among the first you will come out with, and I seriously doubt "non-square" will be mentioned at all.

Even though I expressed "non-square" as a negative, my point is that it can quite easily be defined in a positive way. The non-square feature is equivalent to having an even number of positive divisors. A positive definition for primes is: p is prime if p divides ab implies that either p divides a or p divides b. To conclude that something doesn't count as a legitimate group, it should be impossible to express it positively, which is something that very rarely occurs.

Hix
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Puzzle time again.

Find the next number in the sequence:

1000
1000000000
1000000000000000000000000000
100
1

DiMono
Level: Smitemaster

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0.1?

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Hix
Level: Master Delver

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The 6th number in the sequence is not a power of ten; but the 13th, 14th, 15th, 16th, and 17th are.

DiMono
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Sure it is, it's 10^0

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Schik
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Looks like DiMono can't count.

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DiMono
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Please, I can count at least to 4586934^0!

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Hix
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That beats me. I can only count to 0^4586934.

stigant
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Actually, counting to 0 is quite a feat. It took the human race several millenia of civilisation before they invented (discovered?) 0. Positive integers are easy to find. But the concept of zero, ie nothingness, is very difficult to grasp.

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Fried Chips
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Hix, when you specify that the 13th - 17th numbers are powers of ten, do you mean that the 7th - 12th numbers are NOT powers of ten, or are you simply not giving us that information?

[Edited by Fried Chips at Local Time:02-27-2005 at 11:28 AM]

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Hix
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Ah, yes. In this case, the only powers of ten in the entire sequence are the ones I mentioned.

LeForce
Level: Delver
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4 is next, then 8

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Hix
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Quite right, LeForce. And then 3, and then 5, and then.... Um, the next two are tricky. You probably can't calculate them without some really advanced mathematics, but I figured out the 14 terms after those pretty easily before getting stuck again.

So, Leforce, for solving the puzzle you get a kajillion zillion points, and the honor of giving the next puzzle. (Tag)

stigant
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what was the pattern?

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Hix
Level: Master Delver

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stigant wrote:
what was the pattern?

A clue can be found near the beginning of this cartoon. If you have the patience to watch it for a few minutes, click "No!" when it's over to see an even bigger clue.

DiMono
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I'm not seeing it...

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LeForce
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The pattern was alphabetical,

can someone explain what is wrong with this mathematical progression?

If we let a = b then

a^2 = ab (multiply by a)
a^2 - b^2 = ab - b^2 (subtract b^2)
(a+b)(a-b) = b(a-b) (Factorise)
a+b = b (divide by (a-b))
Since a = b,
b+b = b
and 2b = b
Let b = 1 then 2 = 1

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stigant
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you divided by a-b, but a-b = 0
you can't divide by 0.

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Fried Chips
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Hix wrote:
A clue can be found near the beginning of this cartoon

OK, I got the pattern, but what was the clue? Maybe I'm just being dumb, but I didn't see anything that would be helpful...

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Hix
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Sorry for being so evasive. The clue from the cartoon was supposed to be the use of "jillion" as a number, even though it is not an actual number. I also used "kajillion" and "zillion" in a recent post: These two are not numbers either, but the sequence would have been different if they really were numbers.

DiMono
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No reason to be evasive, now that the puzzle's been solved you can share freely. I still have no idea how the word "kajillion" translates to that pattern of numbers.

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Rabscuttle
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ah!

It's the first number that contains each letter when they are written in words.

One thousand
One billion
One octillion
One hundred
One
Four
Eight
Three

LeForce
Level: Delver
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well done stigant, I really need to think up better puzzles don't I?

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Tim
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Rabscuttle wrote:
One thousand
One billion
One octillion
One hundred
One
Four
Eight
Three

I don't get it. Why not use "Zero" for the fifth one?

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RoboBob3000
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I think positivity is a restriction, because then there'd be no end to negative numbers containing the word "thousand".

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Maurog
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So it's Stigant's turn now, right?

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stigant
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File: mathproblem.bmp (76.3 KB)
Downloaded 157 times.
License: Other
From: Unspecified

Sorry, I was trying to think of a good puzzle, but unfortunatly, I'm a math teacher, so most of the problems I've been playing lately involve some reasonably complicated math. Here's one that you ought to be able to solve with only basic geometric formulae and a moderate amount of ingenuity. See the attached diagram. The areas of the three small triangles are indicated (6, 3, 2). Find the area of the whole triangle.

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