46 replies to this topic

[terry1966]

well done rshaffer4444 not my day, got the answer to both but not in time for first correct.. you wouldn't believe how complicated i was try to make the shapes before i finally got it and reconfirmed to myself what an idiot i was.. just seen your reply tomk, looks like i'll have to go back to the drawing board too then. was convinced that was it.

Edited by terry1966, 25 April 2011 - 05:07 PM.

[Nahumi]

How about this :



Technically each bit of land is the same shape, just a different size. They also start and stop each fence on a post and they aren't mirror images because each shape is symmetrical so therefore can be rotated as well as mirrored.

[Tomk]

@ Nahumi,

I've superimposed the "small" parcel on a big one. Then I "expanded it to match scale down one leg.

Do you still contend that you have complied with the "poor" old man's wish's that all parcels be the same shape?

[terry1966]

yes they are all the same shape, tomk just not size as your pic shows, so what you want is the same shape and size, correct,

[Nahumi]

Okay...how about this ?



Unlike the one before, the proportions are the same for each shape. The larger shapes have been increased by a factor of 2, and again because they're symmetrical you can just rotate them to get the same shapes.

P.S. Are we taking inheritence or death tax into account?

Edited by Nahumi, 25 April 2011 - 06:03 PM.

[chrissy72]

Hey guys Im liking Nahumi's last answer. Well done Nahumi

[terry1966]

no idea how you lot post your images but this is my guess and like Nahumi hinted at earlier, not all the land is used, and the black bits go to waste... or you split them equally and give all four, 2 plots of land not touching each other but all the same size and shape.

[terry1966]

or even this :- where the black parts can be wasted or divided to give 2 plots of land to all 4 but definitely not touching.

oops this doesn't work..

Edited by terry1966, 25 April 2011 - 06:41 PM.

[Tomk]

Okay...how about this ?



Unlike the one before, the proportions are the same for each shape. The larger shapes have been increased by a factor of 2, and again because they're symmetrical you can just rotate them to get the same shapes.

P.S. Are we taking inheritence or death tax into account?

I believe that this answer does satisfy the criteria of the Will.

The parcels are indeed the same shape... size is different but that wasn't a criteria. Each inheritance is equal... just some are more equal than others.

[terry1966]

well done Nahumi, . even if i did think both your last 2 answers fulfilled the criteria of the will, no where did i see it say the bigger plots had to be double the proportion of the small plots, just same shape.

Edited by terry1966, 25 April 2011 - 07:06 PM.

[Tomk]

The criteria said that they must be the same shape. Saying that the plots outlined in post #17 are the same shape is the equivalent of saying that a square and any rectangle are the same shape... or maybe a square and any parallelogram.

[terry1966]

Saying that the plots outlined in post #17 are the same shape is the equivalent of saying that a square and any rectangle are the same shape... or maybe a square and any parallelogram.

actually no it's not. it's saying anything that look similar are the same shape.

just because the proportions are not equal in all doesn't mean they are not the same shape.

all the internal angles are exactly the same, so all sides slope at the same degree,
the sloping sides of each shape are the same length, same for all 4
the sloping lines are connected by parallel lines on all 4
the longest parallel line is longer than the sloping lines on all four.
sounds like the same shape to me..
just depends on how loosely you define shape i suppose.

but the puzzle, and the fun is about finding your solution.
the friendly banter and discussion/disagreements sometimes afterwards is fun too.

many thanks as always,
for providing us with much amusement and hair pulling with these weekly puzzles tomk.
it is sincerely appreciated by all of us who like to try and work them out.

Edited by terry1966, 26 April 2011 - 03:10 AM.

[Sunyata]

I think terry1966 has a point. There is some ambiguity here. The trouble is that the expression "same shape" can have imprecise meaning. Rigidly speaking geometrically, the pentagons are similar. They scale uniformly. On the other hand, all the shapes in Nahumi's first picture are trapezoids. All trapezoids have the "same shape," arguably. Suffices to say that the siblings will probably be in court for many years.

[chrissy72]

but the puzzle, and the fun is about finding your solution.
the friendly banter and discussion/disagreements sometimes afterwards is fun too.

many thanks as always,
for providing us with much amusement and hair pulling with these weekly puzzles tomk.
it is sincerely appreciated by all of us who like to try and work them out.

AGREED

[Tomk]

We have a whole week to debate this.

Consider the following:

All four are Quadrilaterals. are they therefore the same shape?
A and B are Rhombus. Are they then the same shape?
A,C, and D are rectangles. Are they the same?
All 4 are parallelograms.
All 4 are trapezoids.

Can we agree that the only Quadrilateral, Rhombus, Rectangle, Parallelogram, trapezoid is A? Therefore none of the others are the same shape.... though they may share similar characteristics?

So what is a shape?
David George Kendall was a professor at Cambridge University. He was a statistician and an expert on shapes.... specifically as related to statistical shape analysis. I think that he defined it best when he wrote, "Shape is all the geometrical information that remains when location, scale and rotational effects are filtered out from an object." Let's put that in simpler terms. A shape is made up of it's boundaries. "Shape is the lines, and their relationship to each other" Two intersecting lines always form an angle.... but it is their relationship to each other that determines if it is an acute angle or an obtuse one. 4 equal sides set at right angles form a square... rather than just a rectangle or a rhombus, or a trapezoid, ....etc, etc.


C and D are both non Rhombus rectangles. Given that A is a "special" rectangle - a square... let's say that C and D are "regular" rectangles. C is a rectangle with the short leg equal to 1/2 the length of the long leg. D is a rectangle with the short leg 3/5 of the length of the long leg. Are they the same shape? If a shape is the lines and their relationship to each other...Can you describe both of them using the same words?