bonanova

I think there are only six ways four points can collectively have the same max and min distances. In only one case [square] do the points individually have the same max and min. So I think you're condition is correct. Look at post #6 here Look at post #15 [and others] here, also

The English language is weird. Just weird. In this post you are asked to find sixteen of the words and phrases that make it so. This should be fun ... enjoy. First, two comments This post is long. Using QUOTE or REPLY will really chew up screen space. My suggestion is -- don't do it. I've numbered the questions, so that when you give an answer you can put just the answer inside a spoiler and expose just the question number in the spoiler heading. That way you can look for answers to particular questions without seeing all the other answers too. These puzzles are not all mine. Since exposing proper attribution might suggest a search path to find the answers, I've put it in the following spoiler. You can look if you like, of course, but if you want to work these on your own, I've shielded you. Vowels 1. Most consecutive Aqueous and sequoia are words that contain 4 consecutive vowels. Another contains 5 consecutive vowels. What is it? All 5, ordered 2. At least five words contain all five vowels in alphabetical order. Abstemious, abstentious, adventitious and parecious are four of them. The fifth is in common usage. What is it? 3. At least six words contain all five vowels in reverse alphabetical order. Duoliteral, quodliteral and unoriental are three of them. Three others are in more common usage. What are they? Longest words with one vowel [unrepeated and repeated] 4. The longest word with a single [unrepeated] vowel has eight consonants. What is it? 5. The longest words with a single [repeated] vowel have 10 and 13 consonants. What are they? Consonants 6. Most consecutive One word has six consecutive consonants. What is it? 7. Longest word with one consonant [unrepeated] Several five-letter words contain only one [unrepeated] vowel consonant. [edit] Name one of them. General 8. Connect the dots Beijing and Fiji are two proper nouns that contain three consecutive dotted letters. Name another, not capitalized, word that contains three consecutive dotted letters. 9. Alphabetically consecutive letters Two words contain four consecutive letters that are also alphabetically consecutive. What are they? 10. Sound the letters Essay [sA], enemy [NME] and excellency [XLNC] are words whose pronunciation comprise only letter sounds. What word's pronunciation can be accomplished using five letters? 11. Pros and Joes Nouns. Amazingly, five personal pronouns [without scrambling them, and using no other letters] can be juxtaposed and overlapped to form a single common noun. What is the noun? 12. Palindromic words The longest palindromic cluster of letters embedded in an English word is sensuousnes. A final s makes the word itself. The longest palindromic word of all is the arcane eleven-letter chemistry-related detartrated. The longest palindromic word likely to be found in a common dictionary has nine letters. What is it? Bonus: a word whose meaning might be inferred by reversing its letters: Embargo => O grab me! 13. Even and odd Extracting the alternating, even and odd, letters from some words yield two new words. Two of these yield the four words cold, lug, one and shoe. What are the two words that produce them? 14. Triangular words Triangular words have letter counts of 1, 2, 3, 4 ... and thus have a total length that is a triangular number: 1, 3, 6, 10, 15 ... One proper triangular word is Tennessee's - t-1, n-2, s-3 and e-4. Name a 10-letter triangular word that is not capitalized. 15. Typewriter words These are words comprising [with repeats allowed] letters from a single row on a standard keyboard. The longest of these words have ten letters. Two of them are proprietor and perpetuity. What is the third? 16. Pangrams A familiar short sentence [33 letters] that contains all 26 letters is The A quick brown fox jumps over the lazy dog. [edit]* Find one that uses fewer than 33 letters. *Thanks to Browne85 in post #4 for this edit.

Increase B by a letter: What 9 letter word has 8 consonants and 1 vowel?

The frogs will eat any bugs. Your code must include a fairly tight test for "squareness". Care to share that part of it? I ran across a question that asked how efficiently that test could be implemented.

Well I think what's happening is that a single question is being treated as if it were two questions. I would analyze the Commoner's freedom of response like this: [1] The OP states the Commoner is free to answer as he pleases. [2] If he had been asked two questions, he would not have to treat them the same. He could lie to one and tell the truth to the other if that pleased him. [3] He wasn't asked two questions. The OP requires that only a single question be asked. That single question has a single answer. That answer is Yes or No, and the Commoner is free to choose which. I'm not sure what follows "And thus ........." Here's my thinking about the Knave's response. For every assignment of Knght/Knave/Commoner to A/B/C, SCHMOD54's question has a well-defined truthful answer. If the Knight is asked, he will give the truthful answer. If the Knave is asked, he will give the other answer. If the Commoner is asked, he will answer arbitrarily, as he pleases.

Am I right?

Yes. Assume they have full knowledge. The phrase was added because #1 didn't require it.

Four frogs are enjoying their favorite pastime of hopscotch. One of them, Alex by name, proposes a new game. Not surprisingly, it involves a challenge. Look here fellas, he croaked, as he drew four X's on the ground so that they formed the four corners of a square. We all start out on one of these corners. Then we take turns jumping over each other. The object is to end up sitting on new spots that form a larger square. The frog who makes the final jump to form the square is the winner. Here are the rules: [1] We can jump another frog from any distance. [2] We land an equal distance away from the jumped frog: if he's 2 feet away, I land 2 feet beyond him. [3] Jumps are in a straight line: initial position, jumped frog and landing position are in a straight line. One of the other frogs, amazingly named Jamey, wondered why they had to take turns. Maybe I want to think about my next jump for a bit, I don't want to hold up the game. OK, then, we'll jump one at a time, but not necessarily in order, Alex agreed. Can you prove that it's possible to win the game ... or not? If so, how many jumps will it take?

I think you kind of handed it to us. Adding a couple other credible witnesses statements might have hidden his flaws better. I was going to Google Earth the location anyway, tho, to see which coast it was on. Another suggestion [not that you asked ... ] you might have said, "as the shadows of the palms lengthened toward the shore ..." or "reached out to the surf" and "dinner date" without saying "9:00". More subtle, and might invite subjective rather than analytical thought. 'nuff comments - I liked it - and welcome back! Hey - and Kudos to Sandstorm [post #2], who found some things the rest of us didn't mention!

The OP says - You're right in thinking "anything you want" is neither true nor false, so it won't produce a beheading or hanging. But ... since "anything you want" is not an affirmation, the king will simply wait until you do make one. Unless you go through life never again making an affirmation, you'll eventually have to play his game.

The annual Horse racing tournament is a week away. You own 25 horses, and you're allowed to enter up to three. You decide to hold a series of races to find your three fastest horses. You have access to a track that permits five horses to race against each other. Here's the deal: [1] No two of your horses are equally fast - there will be no ties. [2] You have no stopwatch - you can't compare performances from different heats. [3] You do not want to tire the horses needlessly - the fewer heats needed, the better. [4] You want to know which horse is fastest, which is next fastest and which is third-fastest of the 25. How many heats are needed?

Nice job.

Well I think you can't trust him to answer in any way that you can anticipate. I see how "answers as he pleases" might be taken to mean "answers to his advantage", but let's rule that out and assume nothing about his motivation - or that he has no motivation.

I mean "of" in the sense you mean "to". The king asks one suitor two questions.

Nice job!

[1] Standard version of a classic A king wishes to choose the man his daughter will marry. She has three suitors: a Knight, a Knave, and a Commoner - whom the King wants to avoid. The king does not know which man is which, and the suitors do not know each other. But the king knows Knights always speak the truth, Knaves always lie; while Commoners respond as they please. The king asks each man one yes/no question, then chooses the groom. What are his questions, and how should he choose? [2] Standard version with a twist Now suppose the three suitors know each other. Find a new strategy for the king to ask a question of just two of the three suitors to pick the groom. [3] Making it a little harder Find a strategy for the king to ask questions of only one suitor, but there can be two questions. [4] The Puzzle Master special Find a strategy for the king to ask only one yes/no question and only of one suitor. ------------------- Edit for clarity: "ask questions of one suitor" means "ask one suitor a question"

It was his first day as bank teller, and Adam made a big mistake. When Judy handed him a check for $AB.CD, the cash he gave her amounted to $CD.AB instead. When Judy later bought a newspaper for $0.50, she realized the mistake. She also counted her remaining money and found it was exactly 3 times the original amount of the check. What was the value of the check? That is, what are the values [not necessarily different] of A, B, C and D?