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MatPlus.Net Forum General Riddle of the Day

### Riddle of the Day

With an area measuring only 594 x 841 mm, it may reside on a dinner plate, yet it (which is always in the best possible condition) is so vast that that roughly a quarter of all castles settled upon it.

What is it?

And its length is equal to the length of the diagonal of the largest square which can be inscribed therein.

I am drawn in. To this puzzle, I mean. Here's my thinking so far. Many things could be on a dinner plate, like a tennis ball, or even a hula hoop. So it's roughly 23 inches by 33 inches. Hmm, that doesn't ring a bell. I suppose some chessboards could have that dimension, with side areas for captured pieces. And I suppose a "quarter of all castles" could mean one rook out of the standard four in a game. So that leaves me nowhere... Andrew's comment that basically says that 841 is approximately equal to 594 times the square root of 2... also leaves me nowhere... I await to see the answer...

And the amount of rice allocated per square cm for these different sizes of dinner plate can be constant? :-)

A: A1 (a1) ("A1").

"A1" is "vast" (it is a term with many meanings).

1) A1 is a standard size of paper (23-3/8 x 33-1/8 in),
2) A1 is a Steak Sauce (marketing geniuses have removed the words "steak sauce" from the bottle), which was once quite popular (why?),
3) "A1" is defined by Cambridge English Dictionary as: being in "very good or in the best possible condition," and

(drumroll)

4) a1 is a square on the chess board, upon which one of the four original (roughly a quarter of all) castles is settled.

ps: I forgot to add the 5th -- it's a bond rating, though that addition might have presented only challenges (to keep the riddle sound).

pps: Andrew Buchanan, who solved it quite nicely, also suggests a sixth thematic continuation (which I will let him explain).
Thus I have extended an offer of joint credit. :)

ppps: You were on the right track, Mark.

Really this is Kevin's problem: so any use he can make of my nonsense he is welcome to own.

I was thinking of A1 as a paper size. (An from n=0 to 10 see https://www.swiftpublisher.com/useful-articles/paper-sizes-and-formats-explained has area 2^(-n) metres. So a sheet of A2 has half the area of A1. This reminded me of the story about grains of rice on the chessboard, where each square contains twice the number of grains of the square before.

Alas this will cannot be extended beyond the a-file. There are also B & C series of paper sizes, but Bn has 1/sqrt(n) the area of An, while Cn is something different for making envelopes to nicely take A4 pieces of paper. For all of this, the critical constant is 2^(1/4). So an A4 sheet has sides 2^(-7/4) x 2^(-9/4).

Are there any other commonly occurring non-quadratic roots in daily life?

I was, of course, only kidding about credit. You may share this riddle freely, without any memory of where it came from.

I have no intent to use this as the basis to pen "64 Chessboard Riddles," though I welcome any additional entries offered here. :)
Just beware of f7!

QUOTE
Are there any other commonly occurring non-quadratic roots in daily life?

According to google, the standard ice cube is two tablespoons. So the standard ice cube size must be the cubic root of two tablespoons.

Dmitri, do you get your ice cubes at the Deli?
(OK, I can be obscure too ;-)

That was enjoyable! Thanks Kevin.

Okay, here's a quick riddle along the same lines:

"B8," he called out.
"Sorry," he said. "That is not the correct thing to say. You do not win the prize."

(What should she have said?)

I am perplexed, Mark.
My gut is screaming, "BINGO!" LOL.

But, I'm hoping that is wrong.
I will ponder this. Give me a day.

Right you are, Kevin! "Bingo!"

My intention was nothing more royal. Apologies to those who are unfamiliar with the game of bingo. I'm not even sure if the game is played outside the US. Starting with a 5x15 grid, with columns B,I,N,G,O and the B column has numbers 1 through 15, the I column 16 through 30, etc., the caller takes turns pulling out one of the 75 choices from a randomizing basket, and calls out the choice, as in, "N42!" and keeps track on the 5x15 grid which ones have been called. Each player has a 5x5 "bingo card" that have all five columns B,I,N,G,O but only some of the numbers and keeps track of the ones that are called out that are also on the player's card. The first player who gets five in a row, column, or long diagonal, calls out, "bingo!" and after verification, wins a prize. (But no, I doubt if any caller would be so mean as to withhold a prize just because a player called out the wrong thing!)

Mark, I spent the day pondering away, and here my instinct had it right in a flash.

Thank you for providing a this additional entry to the future classic, "64 Chessboard Riddles." :-)
There's a good lesson in that riddle: Do Not Be Quick To Distrust Your Instincts.

"You sank my battleship"?

(15) Posted by Hauke Reddmann [Thursday, Jan 13, 2022 13:19]

@Joost: So did I, especially as "Aloha E" by Neue Heimat is on my mixtape...