On Friday I set this puzzle…
Here is a schematic plan of an orchard, with the green circles representing trees. The orchard belongs to four brothers and they want to split it between them. Can you divide the orchard into four parts, such that each part is the same size and same shape, and has the same number of trees?
If you have not tried to solve it, have a go now. For everyone else, the answer is after the break.
Did you solve it? Any other answers?
Advertisement
Like this:
One blogger likes this post.
September 27, 2010 at 5:30 am |
I had a less swastika like solution, with basically the same L shape.
September 27, 2010 at 5:32 am |
Tetris Skillz!
September 27, 2010 at 5:34 am |
Yes. Same shapes (the L shape is key) but split the square down the muddle. Then take each half and arrange the Ls in them to have the same effect.
This puzzle thus has more than one solution.
September 27, 2010 at 5:38 am |
Like the others I found two solutions, this one with rotational symmetry but also one with horizontal symmetry but still using the L shape.
September 27, 2010 at 5:43 am |
Same as above. Found the other solution first, after realizing an L-shape could work. There’s also a solution with 4 t-shaped pieces
September 27, 2010 at 5:46 am |
Using the top 3 blocks on the left hand side and the one adjacent to the middle one, you form a T-shape with 3 trees. If you rotate the square, you can use the same pattern on each side and have 3 trees each time.
September 27, 2010 at 5:49 am |
I solved it using Ts.
September 27, 2010 at 2:09 pm
Same here. Start with a T on top right.
September 27, 2010 at 6:19 am |
It can also be done with the following shape (the X’s below):
X_
X_
X_
_X
if we’re allowed to tile it so that it overlaps on the non vertical bit.
Other than that, the L and the T are the only solutions.
September 27, 2010 at 6:29 am |
Top line; bottom line; leftmost four of the middle two lines; rightmost four of the middle two lines.
September 27, 2010 at 6:42 am |
I thought you had to have the trees in the same shape and just couldn’t do it….took me forever to give up and reread the puzzle and then found my mistake and then solved it using T shapes.
September 27, 2010 at 6:56 am |
I solved it with making each of the first two columns an i then using l’s for the last two columns.
1233
1243
1243
1244
September 27, 2010 at 7:24 am
@lilabyrd
Instructions state that the shapes all need to be the same.
Found one of the L solutions and the T solution
September 27, 2010 at 7:25 am
I mean @Bradleu
September 27, 2010 at 7:17 am |
solved with T’s as well:
3222
3321
3411
4441
September 27, 2010 at 8:26 am |
Mine http://imgur.com/zwsg6.jpg
September 28, 2010 at 3:41 am
Well the shapes are mirrored dont know if that counts.
Solved it with T-Shapes as well.
September 27, 2010 at 8:29 am |
I used the T solution, took me two tries tho
September 27, 2010 at 8:39 am |
Yep, I got it with Ts, too – after reading all the Tetris comments. I wonder if this is worth a Richard survey – “Are you male or female? Did you think of Ts or Ls? Do you like spinach?”
September 27, 2010 at 9:09 am |
I went for T shapes: http://www.deebster.com/tmp/fri-puz-20100924.html
I’d also got the other L arrangement but as the ‘correct’ answer is often the prettiest, I thought the above would be official.
September 27, 2010 at 5:46 pm
That was my solution as well.
September 27, 2010 at 9:54 am |
I also solved it with T’s
September 27, 2010 at 11:35 am
same.
September 27, 2010 at 10:46 am |
Solved with T’s, got the same solution as Dan. Starting to wonder just how many solutions to this puzzle there are.
September 27, 2010 at 11:54 am |
T’s here (or pyramids as i described them).
Girlfriend saw alternate L solution.
September 27, 2010 at 12:03 pm |
I got both the L and the T solution
September 27, 2010 at 12:23 pm |
At first I though the trees all had to be in the same position within each shape but as soon as I clicked that wasn’t specified I got the other L shape solution.
September 27, 2010 at 12:35 pm |
I found three patterns: http://twitpic.com/2shwa9
September 27, 2010 at 1:05 pm
Notice that your third solution does not satisfy the requirements of the puzzle. The plots are not all the same shape. The L’s on the left are mirror images of those on the right.
I think that many of the solutions proposed have the same problem. The only 2 solutions I could find that strictly satisfy the requirements are the posted solution and the T solution.
September 27, 2010 at 1:47 pm
It could be a mirror image or is could be the same shape viewed from the other side.
September 27, 2010 at 12:46 pm |
nah, i thought trees where a part of the shape and couldn’t solve it,
September 27, 2010 at 12:51 pm |
I found the L solution.
I also played with non-contiguous plot shapes, since the puzzle didn’t say that they had to be contiguous, but couldn’t find any.
September 27, 2010 at 12:55 pm |
An interesting exercise would be to come up with a puzzle containing a single solution where the arrangement of trees needed to be the samein each shape as well. Or, a puzzle where there would be exactly two solutions (again where the trees needed to have the same placement as well) that could be solved with two different shape configurations.
September 27, 2010 at 2:22 pm |
I solved with L’s first then spotted the T’s about 10 seconds later
September 27, 2010 at 4:04 pm |
The worst thing about this puzzle is the ridiculou’s quantity of superfluou’s apostrophe’s in the comment’s.
September 27, 2010 at 11:36 pm |
I didn’t get the T solution at all – I stopped after the L that’s shown.
September 28, 2010 at 12:09 am |
[...] Answer to the Friday Puzzle….. On Friday I set this puzzle… Here is a schematic plan of an orchard, with the green circles representing trees. [...] [...]
September 28, 2010 at 12:15 am |
I found one additional solution besides the Ts and Ls.
1234
1234
2143
2143
It could be argued that the shapes aren’t the same since they are mirror images, but I would argue that the “shape” is the same.
Also, some might argue that they make more than 4 parts, but the lots would touch at an infinitely small point.
September 28, 2010 at 6:19 am |
Lots of solutions and lots of solvers!
It seems that this is pretty easy. For me it comes down to the start point; as soon as you know that the shape has to be four blocks and contain 3 trees (which some seems to do in seconds), it’s pretty easy.
Nice though!
September 28, 2010 at 10:11 pm |
[...] Answer to the Friday Puzzle….. « Richard Wiseman's Blog [...]
September 28, 2010 at 10:20 pm |
[...] Aחѕwеr tο tһе Friday Puzzle….. « Richard Wiseman's Blog [...]
September 30, 2010 at 10:15 am |
Are reflections of non-symmetric shapes, such as b and d, the “same shape” or not? I would say that they are of the same shape but of opposite parity.
December 13, 2010 at 9:35 am |
1122
1342
1342
3344
I think there are lots of solutions.
December 30, 2010 at 3:58 pm |
This is how i solved it http://i54.tinypic.com/25qarv4.jpg