Determine whether there exists a function $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$f\big(x^3+x\big)\le x\le\big(f(x)\big)^3+f(x)$$ for all $x\in\mathbb{R}$.
Source: Math Excalibur Volume 22 No. 4 Page 3 Problem 536 rephrased
Once again, you have angered the Emperor, and she has imprisoned you in a special prison.
“I do have a bit of good news for you,” the Emperor has told you. “You're only two doors away from freedom, and I've left all the doors unlocked for you!” Of course, she neglected to mention the details.
S...
This Welsh town's northern fair is, after all, very backward: firstly popcorn with lemon; secondly, bloody agility swings; finally, scary clown going away without starting. All agog, very chewy outer layers right now. Selling wares from wardrobes: two ewes, four fifties, inner pants. Outwardly...
I have created a puzzle that includes multiple steps, that I'd like to post on the site. However, two of the steps use standard puzzles as part of making progress.
Assuming I attribute the source, is it fair game for me to find an instance of these standard puzzles on the Internet, or use a p...
@jafe Is al'Thor (the fantasy character or maybe our own) a HIREDHAND perchance? HI + R(E D_ H)AND. AFAIK that's usually written with a space, but so many words are losing their spaces these days. (Though the clue would probably then have "e.g." or the like at the end. And "separately" would be extraneous.)
I looked up his names/titles online, as well as those of his adoptive parents, and none seem to have nine letters. CHARACTER or MODERATOR would seem to require an "e.g." or the like at the end, but I'm certainly willing to consider them as possible solutions anyway.
"My word!" is a CALL. "heroin" is NOR< ("ron"). I don't see a reversal indicator. "a bit of DXM" is D. So "a bit of DXM and heroin separately ingested" could sort of maybe be NDOR if we find a reversal indicator and squint a bit.
Oh, maybe "separately" is "after being separated into its component characters" i.e. an anagram indicator. Then "a bit of DXM and heroin separately ingested" is easily NDOR.
But "Ecstasy" would then have to be A.
. . . which it doesn't seem to be.
> Oh, maybe "separately" is "after being separated into its component characters" i.e. an anagram indicator. Then "a bit of DXM and heroin separately ingested" is easily NDOR.
No, that would be an indirect anagram. Oops.
@Randal'Thor maybe "ingested by Rand al'Thor" could be a definition? Is there an adjective or collective noun referring to what (or whom) he eats/kills/subsumes/is possessed by? (In case you can't tell, I know nothing about this character. I don't even know if this "Wheel of Time" thing is a book or a game or a movie or what - though I'm sure that's easily Googlable.)
I'd been thinking (1) that "Rand al'Thor" might mean ALTHOR*, and (2) that "My word!" might mean some notably Finnish word. But the only 9-letter Finnish greeting I can find is TERVEHDYS and while it does contain an E, an D, and an H, all I can get out of what remains is VESTRY* which seems not very useful.
Taking "Rand" to mean "R and" is a clever idea, though.
anyway, as so often it'll be a little while before I have a replacement. (I don't have a clue bank, though I do have a bunch of failed past attempts and probably some of them are salvageable.)
The 16 words below may be partitioned into 4 groups of 4 connected words.
Additionally, each of the four groups can be represented by a single group-word.
Finally, the four group-words are connected by a single five-letter word.
+--------------+--------------+--------------+--------------+ ...
You are given an empty 6x6 grid. You are allowed to paint some of its cells as walls (black), while the remaining cells stay empty (white). A robot is programmed to start in one corner of the grid and visit the other three corners^ in the least number of steps possible. At each step, the robot mo...
If I place all the numbers from 1 to 9 in a 3x3 grid and I add the products of each row and column, then what is the minimal and the maximal sum?
For example, the sum is 450 on the picture below.
In front of me stands a table with the shape of an equilateral triangle with side lengths 1. I can cover the whole surface with five isometric circular tablecloths. What’s the minimum radius for a tablecloth? (The tablecloths can of course)
If you can solve these, then you probably are one of the Avengers. I find these six random puzzles to be impossible. Any Tony Stark IQs out there (maybe @Deusovi :D)?
Three equilateral triangles with side lengths 28 are placed in the position as shown in the picture above. All the contacts are perfect and a circle passes by exactly one vertex per triangle. What’s the minimal radius?
The game is pretty simple, whoever reaches 50 first wins, but there are a few important details:
2 players, one die. Players take turns.
Rolled values are simply added up
When you roll a 6, however, the sum of the current turn is discarded
When you decide to stop your turn, the current turn's s...
Loosely inspired by the Babson task, here's my first attempt at a Binary Homeworlds problem in the same vein as Simple, Monopoly, Inheritance or Insurance Fraud, and Blastdoor.
Lee (0, g3b2) r1r3g1b1-
Ray (1, r1r3) -y2g3b3
DS1 (y2) b2-r1r3
DS2 (g1) g1g2-
DS3 (g2) y2-
DS4 (b2) r2-g3
The stash...
The set of sixteen words below can be partitioned. Each partition is of four words that have something in common. I invite you to figure out the partitions and commonalities.
ACORN, ALI, BRADLEY, CLEAN, COUNTY, FIRE, HAM, HERSHEY, INNOCENT, IS, LEO, MAMET, MARTIN, RUN, URBAN, VERITE
Once again, you have angered the Emperor, and she has imprisoned you in a special prison.
“I do have a bit of good news for you,” the Emperor has told you. “You're only two doors away from freedom, and I've left all the doors unlocked for you!” Of course, she neglected to mention the details.
S...
This Welsh town's northern fair is, after all, very backward: firstly popcorn with lemon; secondly, bloody agility swings; finally, scary clown going away without starting. All agog, very chewy outer layers right now. Selling wares from wardrobes: two ewes, four fifties, inner pants. Outwardly...
I have created a puzzle that includes multiple steps, that I'd like to post on the site. However, two of the steps use standard puzzles as part of making progress.
Assuming I attribute the source, is it fair game for me to find an instance of these standard puzzles on the Internet, or use a p...
The 16 words below may be partitioned into 4 groups of 4 connected words.
Additionally, each of the four groups can be represented by a single group-word.
Finally, the four group-words are connected by a single five-letter word.
+--------------+--------------+--------------+--------------+ ...
If I place all the numbers from 1 to 9 in a 3x3 grid and I add the products of each row and column, then what is the minimal and the maximal sum?
For example, the sum is 450 on the picture below.
In front of me stands a table with the shape of an equilateral triangle with side lengths 1. I can cover the whole surface with five isometric circular tablecloths. What’s the minimum radius for a tablecloth? (The tablecloths can of course)
If you can solve these, then you probably are one of the Avengers. I find these six random puzzles to be impossible. Any Tony Stark IQs out there (maybe @Deusovi :D)?
The game is pretty simple, whoever reaches 50 first wins, but there are a few important details:
2 players, one die. Players take turns.
Rolled values are simply added up
When you roll a 6, however, the sum of the current turn is discarded
When you decide to stop your turn, the current turn's s...
Loosely inspired by the Babson task, here's my first attempt at a Binary Homeworlds problem in the same vein as Simple, Monopoly, Inheritance or Insurance Fraud, and Blastdoor.
Lee (0, g3b2) r1r3g1b1-
Ray (1, r1r3) -y2g3b3
DS1 (y2) b2-r1r3
DS2 (g1) g1g2-
DS3 (g2) y2-
DS4 (b2) r2-g3
The stash...
The set of sixteen words below can be partitioned. Each partition is of four words that have something in common. I invite you to figure out the partitions and commonalities.
ACORN, ALI, BRADLEY, CLEAN, COUNTY, FIRE, HAM, HERSHEY, INNOCENT, IS, LEO, MAMET, MARTIN, RUN, URBAN, VERITE
