The worlds first riddle!

TehMeh:

Let x be the # of acres on the first day.
2x is second day and so forth.
2^8*(x)=70,000

x = approximately 273.44 acres.

Seems too easy though


It is as easy as your ability allows. :wink:



BOWTTELE


PDANRETRY

BOWTTELE = Wine Bottle

dinner party.....when

oohh Try
I thought I would give you a present for Christmas. Let me know what's in that blue box when you open it, okay and since you couldn't see the Christmas card......





[size=27] MERRY CHRISTMAS & HAPPY HOLIDAYS TRY, BLUE GUY [/size]

Oh please, stop, enough already! I have so much and yet you have none. All these years I and cannot post a picture to return your kindness, so have a song:

Have yourself a merry little Christmas,
Let your heart be light
From now on,
Your troubles will be out of sight
Have yourself a merry little Christmas,
Make the Yule-tide gay,
From now on,
Your troubles will be miles away.

Here we are as in olden days,
happy golden days of yore.
Faithful friends who are dear to us
gather near to us once more.

Through the years we all will be together
If A2K will allow
Hang a shining star upon the highest bough.
And have yourself a merry little Christmas now.

Thank you Try. Has anyone told you lately that you are sweet and you have a RED NOSE

Well in return, I have a cyber kiss for you notice it is only on your cheek and I do have lipstick on

The last time someone called me sweet, was when I fell into a vat of molasses.

Well that kiss brought a smile to my face; so I suppose I should give you back your purse.

Miss mi:

BOWTTELE = Wine Bottle


TTH:

PDANRETRY = dinner party



In how many ways can the number 2007 be written as the sum of consecutive positive integers


(For the daring-doers: In how many ways can the positive integer n be written as the sum of consecutive k positive integers? (As the sum of k arbitrary integers )

I cannot believe you dumped my (what is that thing down there called?) - TAG LINE! I am the dumper - not the dumpee!

He probably didn't mismi40. It disappears when you make an edit to a post. I noticed it was gone a couple of days ago or more, then he put it back. Good post btw

oohhh except I can imagine a come back to this

I can only seem to find 5 ways... I thought I had 6, but I'm not so sure anymore.



I'm not that daring

Oh I am waiting to see what he has to say about that... but I left it in anyway - deserve whatever I get I suppose! :wink:

For a given k, it will be 0 or 1 because there can be at most one sum of length k that equals n.
m + (m+1) + ... + (m+k-1) = (k^2 + k)/2 + (m-1)*k = k * (k + 2*m - 1) / 2
Therefore, k must divide 2*n (and m must be greater than or equal to zero) for there to be a solution.

For all k, the number must be less than or equal to the number of factors of 2*n (see above) since each factor will yield 0 or 1 solution(s).


If the arbitrary integers aren't constrained to be positive, then there are an infinite number of solutions. Assuming they must be postive, must they be distinct?

TehMeh:

Number 2007
I can only seem to find 5 ways... I thought I had 6, but I'm not so sure anymore.

There are five ways to write 2007 as the sum of consecutive positive integers (six if you count the trivial one-term sum).


Daring-doers:

"I'm not that daring"

Very wise!


Mark:

In how many ways can the positive integer n be written as the sum of consecutive k positive integers?

For a given k, it will be 0 or 1 because there can be at most one sum of length k that equals n.
m + (m+1) + ... + (m+k-1) = (k^2 + k)/2 + (m-1)*k = k * (k + 2*m - 1) / 2
Therefore, k must divide 2*n (and m must be greater than or equal to zero) for there to be a solution.

For all k, the number must be less than or equal to the number of factors of 2*n (see above) since each factor will yield 0 or 1 solution(s).

As the sum of k arbitrary integers?

If the arbitrary integers aren't constrained to be positive, then there are an infinite number of solutions. Assuming they must be positive, must they be distinct?


Adding the k integers starting with s yields k(2s+k-1)/2. For this to equal 2007, k must be a divisor of 4014. For six of the possible values of k (including 1), the corresponding value of s is positive.



Miss mi rather amusingly wrote,

"I cannot believe you dumped my (what is that thing down there called?) - TAG LINE! I am the dumper - not the dumpee!"


Honey, I don't care how dumpy you are; you are still on my Christmas card list!

As for what that thing is called; would a Rose look any less beautiful called by another name! :wink:

Now you see it: Now you don't!
TTH writes, "He probably didn't …..It disappears when you make…a post. I noticed it was gone …then he put it back.

So where is it now?



CHCAAUOSGS

KLED

[size=7]causing chaos

linked[/size]

Honey, I don't care how dumpy you are; you are still on my Christmas card list!

As for what that thing is called; would a Rose look any less beautiful called by another name!

really rather mild I'd say...I left the door wide open :wink:

Miss mi writes, "really rather mild I'd say..."

I know, you made it too easy! Where's the challenge? :wink:


"I left the door wide open"

That was the problem... I like to knock a few times before entering!

It's back! You know I was just kidding - you can dump my tag line - don't have to keep it forever

It was only a system malfunction and I'm glad it's back. Although I am toying with:



You don't meet words like that often!

Now I've gotta come up with today's riddle.

Mark:

CHCAAUOSGS = causing chaos

KLED = linked

How the heck did you get that one?



I was just thinking; how many triangles are there with integer sides and perimeter 2007

How many of these are equilateral

How any are isosceles

How many are scalene, i.e., neither of the first two kinds

2007 TRIANGLES
[size=7]I get:
84169 triangles
502 isosceles (including equilateral)
1 equilateral
83667 scalene

0 right
26880 acute
57289 obtuse[/size]