The worlds first riddle!

31 boxes will be open - corresponding to the 31 square numbers less than 1000. Each box gets toggled once per divisor. Only squares have an odd number of divisors.

Stocking filler:

1:45

XXSpadeMasterXX NB

Ahh thank you! I misread and thought it just said every third kid, and every forth kid...etc...Thanks so much! Thought it was just a trick question riddle...

Till New Year? I'll be kind enough to throw a bone for you, just to avoid anyone's brain into becoming decrepit by the time you're back.

If D, E, and F are digits, the the three digit numbers DEF and FED are called a mirror pair. An example of a mirror pair would be754 and 457. There are 2 mirror pairs of 4 digit numbers so that the product of the numbers of each pair is 63504. One of them is 252 and 252 because 252*252=63504. Knowing that, what is the sum of 2 arithmetic values of another mirror pair that when multiplied is 63504?

Fixed an obvious small mistake...
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If D, E, and F are digits, the the three digit numbers DEF and FED are called a mirror pair. An example of a mirror pair would be754 and 457. There are 2 mirror pairs of four 3 digit numbers so that the product of the numbers of each pair is 63504. One of them is 252 and 252 because 252*252=63504. Knowing that, what is the sum of 2 arithmetic values of another mirror pair that when multiplied is 63504?

RIDDLE OF UGGG

Ugg ask
"What brown and sound like ringing rock?"








DUUUUNNNNNGG

144+441=585

Congratulations, that is correct.

I know some of you out there likes chess, so this is for anyone thinking about what a chess is or for anyone who loves the game for what it is.
In an eight by eight chess board, three indiscernible rooks are placed. What is the number of possible arrangements where the three indiscernible rooks can be placed on the eight by eight board such that no two rooks are in a position to attack each other?

8^2 * 7^2 * 6^2 / 3! = 18816

For NxN with R rooks, it would be:
C(N,R)^2 * R!
where C(N,R) = N!/((N-R)! * R!)

My master bids me to answer make in his stead; draw near and lend me your ears…


Markr:

“31 boxes will be open”

Indeed they will...
The only boxes that remain open are perfect squares (1, 4, 9, 16, etc) because they are the only numbers divisible by an odd number of whole numbers; every factor other than the number's square root is paired up with another.

Thus, these boxes will be 'changed' an odd number of times, which means they will be left open. All the other numbers are divisible by an even number of factors and will consequently end up closed.

So the number of open boxes is the number of perfect squares less than or equal to one thousand. These numbers are one squared, two squared, three squared, four squared, and so on, up to thirty one squared. (Thirty two squared is greater than one thousand, and therefore out of range.) So the answer is thirty one.

All numbers with odd number of factors will be open, so all perfect squares less than 1000 will be open.

Therefore the number of open boxes must =31 since 31^2=961 the highest perfect square less than 1000.


“1:45”

Indeed it was...
Markr gave away a total of 25 cents. He divided it between two people. Therefore, he gave a quarter to two.


Thank you Spike, well spotted; welcome to the brain factory and don’t you be a stranger now.


Unlucky Ace (of spades) “Thought it was just a trick question riddle...”

Sir, if I may reiterate the scriptures, “For the appeal we make does not spring from error or impure motives, nor are we trying to trick you.”

1 Thessalonians 2:2-4



My Dear Bennet, perchance your first name is ‘Gordon’ maybe?
I have heard the expression of the name used in Scotland and is indicative of ‘surprise’; although he was the son of the founder of the New York Herald. Quelle surprise!

It is a most pleasant experience to note your visit and question; new contributions are always most welcome. Should you pose one that Markr is not able to answer correctly – the keys to the executive A>K bathroom are yours for the taking.

In answer to your question and following Mark’s answer: 441*144 = 63504


Goodness gracious how mordacious, sorry; that should be ‘audacious’; I am surprised and delighted to see Farmerdude paying us a visit!

Well, dang me if that don’t beat all. You set us a riddle…
Assuming the answer ain’t a pair metal studded UGG boots; then I would guess:

A rock called ‘diabase’

Iffin’ I’m right, please leave a Christmas* Hamper in A>K reception – Thank you.

Iffin’ I’m wrong; leave two – I will need to drown my sorrows!


*(Are you allowed to write ‘Christmas’ on this site without getting banned?)

Should you fear you will succumb to the temptations of the flesh while pondering; stand aside and let me handle it!


Today’s filibuster:

What may I ask is the square root of -16 times the square root of -4 times -1 minus 6 divided by 2?

Answers on a ‘greenback’- Thank you kindly.

Assuming the operations are taken in the order specified:
1
If the division is done before the subtraction:
5

Correct markr!

For the Star War Fans, or the strategist, a riddle to please.
Darth Vader must send a five letter message to the Rebell Alliance. In the message, each letter is a lower case character, and the same letter may turn up more than once in the five character message. When beamed into hyperspace, the letters come out in a random order at the receiving end. Darth Vader chooses his message so that the Rebel Alliance have at least a 1/2 chance of getting the same message he sent. How many distinct messages could Darth Vader send?

26
aaaaa, bbbbb, ..., zzzzz
Obviously, the probability that the received message matches the sent message is 1.
The next best you can do is 4 of one letter and 1 of a second letter, but then the probability drops to 1/5.

Correct markr!

So close , well done.

The order of operations predicates that the answer is 5.

There are quite a few mathematical questions that no-one has been capable of solving yet. Given the quarter is a coin not a combination of coins despite the amusing pun perhaps the time is between 2:10 and 15.

Happy new year already.

Hey Try
What is the call sign when the Pres. and VP. ride together in the same vehicle? I wrote it on the Marb... contest.