Starmaker: ಠ_ಠ
There's enough data to solve the equation without resorting to such uncivilized methods.

Starmaker: Seven dwarves have a keg with 12 pints of beer. They pour it into their 7 tankards, only to notice it hasn't been shared equally. Thus, in the interest of fairness, one dwarf rises and shares the beer out of his tankard equally between the other six. Then his neighbor does the same (again between the other 6 dwarves), etc, etc. After the 7th dwarf has shared the contents of his tankard, it turns out everyone has as much beer as he had initially.

How much beer does each of the 7 dwarves have?

Starmaker: Seven dwarves have a keg with 12 pints of beer. They pour it into their 7 tankards, only to notice it hasn't been shared equally. Thus, in the interest of fairness, one dwarf rises and shares the beer out of his tankard equally between the other six. Then his neighbor does the same (again between the other 6 dwarves), etc, etc. After the 7th dwarf has shared the contents of his tankard, it turns out everyone has as much beer as he had initially.

How much beer does each of the 7 dwarves have?

Starmaker: They don't drink (yet), and yes, one tankard was initially empty. (And the keg has been emptied, too. There's no gotcha.)

Cavalary: Don't think that works, as an ever increasing amount will be shared out if they start from the same value.

trentonlf: If one tankard was initially empty then it was 6 tankards at the start that had liquid in it, so the lone empty tankard would be why they were not all even at the start. I could have it all wrong, but that sounds right to me.

Falkenherz: I think I got it: Starting from the first dwarf, each of the following dwarves must have 1/6 of the amount of beer in the first tankard less beer in his tankard than the previous dwarf. Or in other words:

Dwarf one has 6/21 of the 12 pints in his tankard.
Dwarf two has 5/21 of the 12 pints in his tankard.
Dwarf three has 4/21 of the 12 pints in his tankard.
Dwarf four has 3/21 of the 12 pints in his tankard.
Dwarf five has 2/21 of the 12 pints in his tankard.
Dwarf six has 1/21 of the 12 pints in his tankard.
Dwarf seven has 0/21 of the 12 pints in his tankard.

Edit: So, after the first dwarf has sharded his beer, it looks as follows:
Dwarf one has 0/21 of the 12 pints in his tankard.
Dwarf two has 6/21 of the 12 pints in his tankard.
Dwarf three has 5/21 of the 12 pints in his tankard.
Dwarf four has 4/21 of the 12 pints in his tankard.
Dwarf five has 3/21 of the 12 pints in his tankard.
Dwarf six has 2/21 of the 12 pints in his tankard.
Dwarf seven has 1/21 of the 12 pints in his tankard.

And so on ...

Bascially, they are only circling around all the beer once.

Falkenherz: Assuming that this solution is indeed the correct one, here is my puzzle which I made up half a life ago and which I think is super-awesome. Also, I have to go to bed now, so I won’t be able to check back for the next couple of hours.

Epitaph666: ok so i've set

x = the number of camels (therefore also the number of donkeys)
and
y = the number of camels left after he sold all but 7 of his pets.
therefore the number of donkeys left would be (7 - y)

sO the equation i have is

x * 1 + x * 2 = (x - y) * 2.2 + [x - (7 - y)] * 1.1

And i can't find a second equation for my y. or x...

Falkenherz: Assuming that this solution is indeed the correct one, here is my puzzle which I made up half a life ago and which I think is super-awesome. Also, I have to go to bed now, so I won’t be able to check back for the next couple of hours.
_________________________________________

A king has six daughters. Each daughter has her own room in the palace. These rooms are arranged equally spaced around a six-sided inner courtyard, one room on each of the six sides. Each of the rooms opens out onto a balcony overlooking the yard, with a huge oak tree in the middle of the yard.

All of the daughters ask their father to plant three flower beds under each of their balconies. The oak tree in the middle of the yard prevents each daughter from seeing the nine flower beds on the opposite site of the yard, but each can see the three flower beds beneath her balcony and the six flower beds of her neighbouring sisters.

As it happens, each daughter has two favouritee flowers and one that she absolutely hates. Each daughter requests that each of her favourite flowers stands on at least one of the flower beds that she can see. Also, each daughter wants there to be at least three flower beds within her sight that have one of her favourite flowers on it. However, each daughter also requests that the flower she hates stands on none of the flower beds that she can see. Furthermore, each daughter wants to have three different flower beds underneath her balcony. (Each flower bed can only have one sort of flower on it.)

The clockwise order of the rooms of the six daughters around the inner yard is: Anne, Barbara, Christine, Diana, Ellen, and Fiona.

Anne loves roses and violets but hates lilies.
Barbara loves daffodils and daisies but hates tulips.
Christine loves daisies and lilies but hates violets.
Diana loves tulips and roses but hates daffodils.
Ellen loves violets and daffodils but hates roses.
Fiona loves lilies and tulips but hates daisies.

The king is a very generous father and wants to fulfil the wishes of his daughters. But he is also somewhat greedy and does not want to spend more money on the flower beds than necessary.

What is the lowest amount of gold the king has to pay for the requested flower beds if the costs are as follows and if only these flowers are available:

A rose bed costs 60 gold.
A tulip bed costs 55 gold.
A lily bed costs 50 gold.
A daffodil bed costs 45 gold.
A violet bed costs 40 gold.
A daisy bed costs 35 gold.

grimwerk: Your equation is accurate. The other constraint is that there are an even number of camels.

Simplifying your equation, we get:
10x + 20x = 22x - 22y + 11x - 77 + 11y
30x = 33x -11y - 77
0 = 3x - 11y -77
3x = 11y + 77

Now, note that x is a whole number (we can't have partial camels), and that y must be between 0 and 7, inclusive. There are two values for y that work: 2 and 5. Each results in 11y + 77 being a multiple of 3. Then, recall that x must also be even (donkeys come in pairs, same number of camels). Only y=5 results in an even x (that is, 11y + 77 is a multiple of 6).

Starmaker said the same, but was a bit more terse.

Falkenherz: Assuming that this solution is indeed the correct one, here is my puzzle which I made up half a life ago and which I think is super-awesome. Also, I have to go to bed now, so I won’t be able to check back for the next couple of hours.
_________________________________________

A king has six daughters. Each daughter has her own room in the palace. These rooms are arranged equally spaced around a six-sided inner courtyard, one room on each of the six sides. Each of the rooms opens out onto a balcony overlooking the yard, with a huge oak tree in the middle of the yard.

All of the daughters ask their father to plant three flower beds under each of their balconies. The oak tree in the middle of the yard prevents each daughter from seeing the nine flower beds on the opposite site of the yard, but each can see the three flower beds beneath her balcony and the six flower beds of her neighbouring sisters.

As it happens, each daughter has two favouritee flowers and one that she absolutely hates. Each daughter requests that each of her favourite flowers stands on at least one of the flower beds that she can see. Also, each daughter wants there to be at least three flower beds within her sight that have one of her favourite flowers on it. However, each daughter also requests that the flower she hates stands on none of the flower beds that she can see. Furthermore, each daughter wants to have three different flower beds underneath her balcony. (Each flower bed can only have one sort of flower on it.)

The clockwise order of the rooms of the six daughters around the inner yard is: Anne, Barbara, Christine, Diana, Ellen, and Fiona.

Anne loves roses and violets but hates lilies.
Barbara loves daffodils and daisies but hates tulips.
Christine loves daisies and lilies but hates violets.
Diana loves tulips and roses but hates daffodils.
Ellen loves violets and daffodils but hates roses.
Fiona loves lilies and tulips but hates daisies.

The king is a very generous father and wants to fulfil the wishes of his daughters. But he is also somewhat greedy and does not want to spend more money on the flower beds than necessary.

What is the lowest amount of gold the king has to pay for the requested flower beds if the costs are as follows and if only these flowers are available:

A rose bed costs 60 gold.
A tulip bed costs 55 gold.
A lily bed costs 50 gold.
A daffodil bed costs 45 gold.
A violet bed costs 40 gold.
A daisy bed costs 35 gold.