Puzzling Ducks

• So many creative answers!

The correct answer we were looking for was a 5 pointed star with a pentagon in the middle, like many of you guessed.

Answers where William had too many glasses of bubbles, or reflections on the water were also counted as correct answers.

With 3 winners, here are the lucky numbers:
35, 82 and 25. And so Gold prize goes to:

• Boxcar William from S202 Loch Ness
• Cabovi from com2 Loch Ness
• Lwyrup from US01 Crankshaft

Congratulations to our winners - choo choo! And thank you everyone for participating!

🚂 Welcome Wagon: Tour the ForumIs this your first time here? Then follow me!

• Fine. I am late, but at least I have the right answer.

My ducks are less anal than everyone elses ducks, and prefer more abstract bath tubs.

They are also more mathematically bent.

So they know

the first line needs 4 ducks.
the second line can share only one duck unless we are in a non Euclidean space. Technically, we DO live in a non-Euclidean space, buuuuuuttttttt.... Lets assume a Euclidean space.
the second line needs 3 more ducks
the third line then can share two ducks, but not three (Euclid again)
the forth line can share three ducks, because... Euclidean reasons
the final line can share 4 ducks.

4+3+2+1 = 10

So the first four ducks lined up.
Then the next three lined up sharing one duck on the first line
then 2 more lined up sharing a duck on line 1 and line 2
the last duck lined up with a duck on lines 1,2 and 3

Finally... four ducks moved up and down their lines until they lined up.

Voila...

Modern Art!

• The gravity of the first solution left me more puzzled then the ducks ever were.

Oh well i am mathematically bent like your ducks,might as well be puzzled like them..or by them

• EXACTLY... gravity is why we live in a non-Euclidean world! But you knew that already.

Anyway. The simple set of instructions.

1. Draw a line
2. Draw a line that intersects the prior lines but not at any prior crossing
3. Repeat step 2 as many times as you have ducks in a line (i.e. this puzzle said 5 lines with 4 docks in a row, so repeat step 2 four times)

Euclid stuff...
Euclidean Geometry assumes a flat two dimensional world. A flat piece of paper. In that world. Lines can only intersect (share a duck) at one point.

In a non- Euclidean world, all those rules are broken. For example, if you wrap that piece of paper around the earth, lines can intersect on two points (sharing two ducks per line) think the prime meridian and the equator.

Gravity....
Einstein posited that gravity warps our world from a nice flat 3 dimension piece of paper, into a non-Euclidean space. So you see... you were right!