The goat can eat an area created by the intersection of a circle radius R (the length of the rope) and the circle of the field (radius r). The eating area (E) consists of a segment of the new circle, say angle 2a (a in rads, also call pi p, and let b be the complimentary angle to a). E = R^2.a plus two areas behind the chords in the ‘field’. The area of the chords is r^2.b minus the two triangles height r.cos(b) and base r.sin(b), or r^2.sinb.cosb. Also R=2.r.sin(b) so putting E equal to half of the field we get: (2rsinb)^2.(p/2-b) + 2r^2(b-sinb.cosb) = p.r^2/2
Divide through by r^2 to get 4(sinb)^2.(p/2-b) +2(b – sinb.cos.b) -p/2 = 0 Not elegant, but solvable on a TI-83, and you get b is about 0.61767 rads, so 2sinb is 1.15827 which is the ratio of R to r, i.e the Rope must be about 116m long, as far any farmer cares.
Heard this puzzle years ago and it took me a while to figure it out but alot of you have got it the wrong way round.
the answer is simple:
The meal DIDN’T cost $30 it cost $25 so the correct way of saying the answer is three ladys paid $9 which means they paid $27 in total LESS the $2 the waiter kept equals $25 which was the price of the meal.
You subtract the amount the waiter kept from the total not add it because it’s money that was taken
Once the waiter took the 2 coins, he was officially involved in the transaction and for the sake of ease will become a payee (Who for some reason gets his whole input back). So he must be involved now into the equasion too.
The bill is 25 coins. The ladies PLUS the waiter paid a total of 10 coins each, even if the waiter only put a small amount in (2 coins) it must be divided in that way. So the three ladies paid 8.333* in the bill,
and the waiter kept an equal fraction of the 3 way split change .666*.
(It’s basicaly about reversing what was done in the question and this is a totally irrelevant and long answer)
The ladies split the 28 coin bill, (Due to the waiter stealing 2 coins) so that now must be divided by three, which equals 9.333*. The waiter won’t divide his 2 dollars because it’s unnecessary.
Well, of course there is an infinitely small fraction lost in the time and space continuum, but we shall forget about that. The basic problem is the way in which the question was asked and the fact that you can not divide a round number by three.
[...] eine Reihe verschiedener Bilder mit verborgenen Objekten, darunter auch alte Liebig-Bilder und ein Toblerone-Bild. Ich wusste ja gar nicht, dass auf der Packung Toblerone der Berner Bär versteckt ist. Da werde [...]
[...] Sehen Sie auf dem obigen Bild sieben Delphine? Wer solche und andere Bilder mag, soll die “Hidden objects puzzles” auf Smartkit anschauen. Es gibt eine Reihe verschiedener Bilder mit verborgenen Objekten, darunter auch alte Liebig-Bilder und ein Toblerone-Bild. Ich wusste ja gar nicht, dass auf der Packung Toblerone der Berner Bär versteckt ist. Da werde ich bei der nächsten Packung besser drauf achten. Es gibt auch einige Bilder für Kinder, um die visuelle Wahrnehmung zu trainieren, z.B. traurige Clownsgesichter oder der verborgene Stern. [...]
How old?
she died in 1918 at the age of 62. So her age should be 44 in 1900. 1918 is the only year between 1900 to 1930 that should be divisible by 29.
A certain natural production…
GROWTH
A Lovely Riddle Poem
Read down and up and you will see how i love you if you love me
Swimming Pig
A Dolphin flipping on its back i guess
Hidden in a Fingerprint….
a Dog
Toblerone
its on the mountain with its legs lifted up
Liebig Hidden Object Card
upside down under the tag
Printable Hidden Object in a Fingerprint
i can see a face …but dont know who it is?
Frog Jumping Puzzle
[...] ???? ??? ??????? ?? : ?????? ???? ???? : ?????? [...]
Cube Rotation Question
purple
A scaled word puzzle
level
Hidden Object, Find the Tower Raven
on the pants of tje old man
The missing square: Where does it come from?
[...] The missing square [...]
Sliding cards brain buster
[...] Sliding Cards brain buster [...]
The encircled goat puzzle
The goat can eat an area created by the intersection of a circle radius R (the length of the rope) and the circle of the field (radius r). The eating area (E) consists of a segment of the new circle, say angle 2a (a in rads, also call pi p, and let b be the complimentary angle to a). E = R^2.a plus two areas behind the chords in the ‘field’. The area of the chords is r^2.b minus the two triangles height r.cos(b) and base r.sin(b), or r^2.sinb.cosb. Also R=2.r.sin(b) so putting E equal to half of the field we get: (2rsinb)^2.(p/2-b) + 2r^2(b-sinb.cosb) = p.r^2/2
Divide through by r^2 to get 4(sinb)^2.(p/2-b) +2(b – sinb.cos.b) -p/2 = 0 Not elegant, but solvable on a TI-83, and you get b is about 0.61767 rads, so 2sinb is 1.15827 which is the ratio of R to r, i.e the Rope must be about 116m long, as far any farmer cares.
Puzzle Sum, Guess the Animal
worm
Swimming Pig
a shark upside down
Mini-Mystery by Stan Smith
when will the solution be revealed?
River Crossing Puzzle
[...] http://www.smart-kit.com/s888/.....zzle-hard/ [...]
Simple puzzle will confuse all but the accountants
Heard this puzzle years ago and it took me a while to figure it out but alot of you have got it the wrong way round.
the answer is simple:
The meal DIDN’T cost $30 it cost $25 so the correct way of saying the answer is three ladys paid $9 which means they paid $27 in total LESS the $2 the waiter kept equals $25 which was the price of the meal.
You subtract the amount the waiter kept from the total not add it because it’s money that was taken
School Musical Math Problem
[...] http://pbskids.org/cyberchase/.....rn-player/ http://www.smart-kit.com/s7477.....h-problem/ [...]
How old?
She’d be 44 in 1900 and 74 in 1930 (the year she expired?).
Mark Your Calandars
Yeay! “No Repeating Digits Day” is today!
Simple puzzle will confuse all but the accountants
Once the waiter took the 2 coins, he was officially involved in the transaction and for the sake of ease will become a payee (Who for some reason gets his whole input back). So he must be involved now into the equasion too.
The bill is 25 coins. The ladies PLUS the waiter paid a total of 10 coins each, even if the waiter only put a small amount in (2 coins) it must be divided in that way. So the three ladies paid 8.333* in the bill,
and the waiter kept an equal fraction of the 3 way split change .666*.
(It’s basicaly about reversing what was done in the question and this is a totally irrelevant and long answer)
The ladies split the 28 coin bill, (Due to the waiter stealing 2 coins) so that now must be divided by three, which equals 9.333*. The waiter won’t divide his 2 dollars because it’s unnecessary.
Well, of course there is an infinitely small fraction lost in the time and space continuum, but we shall forget about that. The basic problem is the way in which the question was asked and the fact that you can not divide a round number by three.
Toblerone
[...] eine Reihe verschiedener Bilder mit verborgenen Objekten, darunter auch alte Liebig-Bilder und ein Toblerone-Bild. Ich wusste ja gar nicht, dass auf der Packung Toblerone der Berner Bär versteckt ist. Da werde [...]
Hidden Star
[...] Sehen Sie auf dem obigen Bild sieben Delphine? Wer solche und andere Bilder mag, soll die “Hidden objects puzzles” auf Smartkit anschauen. Es gibt eine Reihe verschiedener Bilder mit verborgenen Objekten, darunter auch alte Liebig-Bilder und ein Toblerone-Bild. Ich wusste ja gar nicht, dass auf der Packung Toblerone der Berner Bär versteckt ist. Da werde ich bei der nächsten Packung besser drauf achten. Es gibt auch einige Bilder für Kinder, um die visuelle Wahrnehmung zu trainieren, z.B. traurige Clownsgesichter oder der verborgene Stern. [...]
Where art meets puzzle: Find the 7 dolphins, horses, and hearts
[...] Sie auf dem obigen Bild sieben Delphine? Wer solche und andere Bilder mag, soll die “Hidden objects puzzles” auf Smartkit [...]
Cutting into 7 pieces
Just cut it six times one after the other, after each rectangle. Six cuts is going to yield seven pieces!
Stately Word Puzzle
REPUBLIC, very nice puzzle, but easy
River Crossing Puzzle
[...] River Crossing Puzzle [...]