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#126 Re: Puzzles and Games » Word Game #66 » 2010-05-16 00:07:07

POSITION AT END OF ROUND 7

Valid words: (rover ears lank rice end)

POINTS:
ZHero........................ 3 (end)
mathsyperson........... 1
JaneFairfax............... 1

#127 Euler Avenue » Gurth's Conjecture » 2010-05-15 22:43:14

gurthbruins
Replies: 10

Gurth's Conjecture:

Consider the following Diophantine Equation:

Find positive integers x, y and z
such that x^2 + 2(y^2) - z = xyz.

My conjecture is as follows:
z = 2(2^n - 1)^2 + (2^n +1)^2  and z = 2(2^n + 1)^2 + (2^n - 1)^2  always lead to solutions.

I did a lot of computing to test z's up to numbers of 40 digits or more.

I submitted my conjecture in January 1990 to David Allison, who was then the number theory specialist in the Department of Mathematics at the University of Cape Town. He took a great interest in this matter, and wrote to me (16 Jan 1990):
"I confess that I am in the same boat as you - I don't see any way to prove this."

It would seem that my conjecture remains a challenge to mathematicians : prove it, or find an example that will disprove it.

I prefer this notation for keyboard use.

#130 Re: Puzzles and Games » Word Game #66 » 2010-05-15 00:41:02

POSITION AT END OF ROUND 6

Valid words: (rover ears lank rice end)

POINTS:
ZHero........................ 3 (end)
mathsyperson........... 1

Note: I've added another word to the list of valid words, as an extra clue.

#131 Re: Puzzles and Games » Word Game #66 » 2010-05-14 00:09:25

POSITION AT END OF ROUND 5

Valid words: (rover ears lank end)

POINTS:
ZHero........................ 2 (end)
mathsyperson........... 1

#132 Re: Puzzles and Games » Metamorphosis » 2010-05-13 09:43:01

No Zhero, ope is correct, not open. (If ope was incorrect, so would oped be).

I always welcome advice, especially when I drive a car. That way I might go through fewer red lights. Even when it is not necessary.
Fun(nily) enough, I just added a signature before I did this post, so presumably it will appear now. I will get around to the avatar soon, I promise.

The Shakespeare quote wasn't meant to be a signature, it was meant to defend my use of the word OPED !!!

#133 Re: Puzzles and Games » Containers of marbles » 2010-05-13 09:25:48

What puzzle are you talking about, where is it and how am I supposed to know the answer to either of these questions... please.

#134 Re: Puzzles and Games » Word Game #66 » 2010-05-13 00:09:00

POSITION AT END OF ROUND 4

Valid words: (rover ears lank end)

POINTS:
ZHero........................ 2 (end)
mathsyperson........... 0

#135 Re: Puzzles and Games » Word Game #66 » 2010-05-12 00:01:36

POSITION AT END OF ROUND 3

Valid words: (rover ears lank end)

POINTS:
ZHero........................ 2 (end)
Mathsyperson........... 0


I was feeling very uncomfortable about disallowing ZHero's word "end". I thought the POD was being downright absurd. I checked in the NEW OXFORD DICTIONARY of 1998 and found it equally absurd.
But I have decided to overrule these stupid dictionaries. SOWPODS (most dear to Scrabble players) allows it and so does even TWL98, the much more conservative American Scrabble dictionary.

So there!

SPECIAL NOTE: From now on players score 2 points for each valid word, plus 1 point for each list they submit. (But remember, only one list per player per day please.)

#136 Re: Puzzles and Games » Word Game #66 » 2010-05-11 00:55:38

POSITION AT END OF ROUND 2

Valid words: (rover ears lank)

ZHero, I swear I thought one of the words in your last list was valid, but on checking my dictionary I found I was mistaken!
Sorry about that!

#137 Re: Puzzles and Games » Word Game #66 » 2010-05-10 20:58:48

Good questions. There is the single, simple rule for valid words that never changes and is pre-defined. Ideally, I should have deposited that rule with an impartial judge. But the game is not serious enough for that.

Then there are also the other rules, which must change in accordance with the needs of the time: for instance the rules about how many words can be submitted, whether inflections and repetitions are valid, how points are scored, and so on.

It is impossible to foresee the dodges or stratagems that players may adopt in order to amuse themselves or to cause trouble, so these other rules cannot be pre-defined.

#138 Re: Puzzles and Games » Word Game #66 » 2010-05-10 20:34:09

"Only one" is a feat that has never yet been bettered, and equalled only a few times. Finding the first matches is not easy! Luck is inspiration...

#139 Re: Puzzles and Games » Word Game #66 » 2010-05-10 19:43:42

ZHero, you will be pleased to hear that you have found a valid word! I won't say which, before noon, because that would be giving other contestants an unfair advantage. (reaping the benefits of your work prematurely)

Every word added to the list of valids will make this problem easier. But I don't look too kindly on the idea that others let you do the spadework and then capitalise on it by pouncing in for the kill.

I am introducing rules to protect the rights of the workers!
But I have encouraged this slacking I suppose by saying that daily entries were not compulsory.

From noon tomorrow, when everybody will have had a whole day in which to see this warning, those players who submit more lists than others will be given a compensatory advantage. You have been warned!

Here is a hint: life may be complex, but this game isn't.
By complex I mean rules involving "and" or "or"
Examples:
Simple rule: "valid words must contain x"
Complex rules: "valid words must contain x or z", "valid words must contain s and c".
This is a simple game: complex rules are undesirable in this type of game.

ZHero: As special reward for activity, and so you do not lose out today because of this hint being given after your entry, you may submit another list today if you like.

#140 Re: Puzzles and Games » Word Game #66 » 2010-05-10 07:11:17

Mathsyperson's list does reveal that the rule does not allow a word to score more than once.

Also I will reveal that inflections such as formed by adding or removing s, d, ing, er  etc will probably not be accepted as valid. (e.g. rove or rovers).
Such efforts may be seen as subversive moves to defeat the ends of justice wink
Other rules may also be changed if it appears necessary. You must rely on my fairness, I have no favourites as I am not a contestant.

#141 Re: Puzzles and Games » Word Game #66 » 2010-05-10 00:23:22

Time to update as promised: ZHero has submitted a list already, but it contains no valid words so the list remains
( rover ears lank ) and there is no score so far.

#142 Re: Dark Discussions at Cafe Infinity » Where can I practice my cryptology? » 2010-05-09 22:31:36

Here's something I just put up on another site yesterday:

ANNH REAT NTSD HOGO FAUC ZPLI AINL MGEB OFIN ONTR GHWH EEEE AAAR VRIET.

- under the title "A Simple Code". Can you solve it?

#143 Re: Puzzles and Games » Metamorphosis » 2010-05-09 21:57:41

Thanks, ZHero, I fixed it now. The Shakespeare too - I didn't mean to use that heterodox spelling.

#144 Re: Puzzles and Games » Metamorphosis » 2010-05-09 21:19:20

Shorter Solution to Challenge 6

SHUT
SHOT
SHOD
SHED
SEED
SPED
APED
OPED
OPEN

"And winking marybuds begin
To ope their golden eyes" - Shakespeare

#145 Re: Puzzles and Games » Us. th. Pe. Ta. of th. El. to so. th. pu. » 2010-05-09 20:51:56

If it's any help, ZHero, I'll solve the Pe. Ta. El. part ... the rest looks like a code to me, I guess you are meant to find letters for the numbers...   "Periodic Table of the Elements", something that exists in Physics or Chemistry.

#146 Re: Puzzles and Games » Word Game #66 » 2010-05-09 20:31:49

I am glad you asked, ZHero, the hidden rule is what you are supposed to deduce from the examples given.

You need to guess what property is shared by the valid words (they all have something in common!) and yet not possessed by the invalid words.  By submitting lists you can try out your hunches, and also stumble on some more valid words by chance or intelligence, in which case the list of valid words will get longer and more suggestive.

#147 Re: Puzzles and Games » Containers of marbles » 2010-05-09 20:14:06

I like your avatar of 5 intersecting cubes! but nobody seems to have a clue about your puzzle: could you give a bit more info? Are those periods representing letters that need to be filled in? In that case my guess is "strumpet". I did not read what you wrote for those who have done this puzzle, as I have not.

#148 Puzzles and Games » Word Game #66 » 2010-05-09 19:48:14

gurthbruins
Replies: 50

In this game, there is a hidden rule which defines valid and invalid words.
Examples of valid words: rover, ears, lank.
Examples of invalid words: eyes, long.

To play this game, post a list of ten words every day. (Doesn't matter if you miss out some days).
All valid words in your lists will be added to the list of valid words which I will update at noon GMT every day.

Every valid word posted scores one point.
The first player to post a list of ten valid words is the winner.

To resolve doubtful words I will use my 1985 Pocket Oxford Dictionary, so better not post very recently coined words.

Have fun!

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