# Listener 4465

Joined: July 16th, 2017, 9:46 am
Another great puzzle, but I snookered myself at the end looking for a synonym for rhombus in the grid.
Doing a Google, hey hey, Little Miss Rhombus appears - bingo!

And there it was in the grid, starting with the top row M the letters M I S S spell out in a diamond shape.
But I was still flummoxed as this was only 18 cells area.

Oh well, beaten again, looking for something that wasn't there :-(
Nick

Joined: October 18th, 2016, 3:57 pm
Luckily I seem to have got this puzzle right. It was a pleasure to see all the four-sided figures in the grid. I was worried because I thought my rhombus covered more than 20 cells in the grid. Maybe someone can explain.

Joined: July 15th, 2017, 9:53 pm
The diagonals of the rhombus are 4√5 × 2√5 and its area is ½(4√5 × 2√5) = 20

Joined: July 16th, 2017, 7:34 pm
Area of rhombus is base times height. Base is 5 and height is 4.

Joined: July 18th, 2017, 8:43 am
Overlaying the mathematical solution on a crossword grid (where we're so used to looking for combinations of discrete cells rather than pure shapes) proved surprisingly tricky. Even having worked out what shape the rhombus needed to be I found myself looking for five cells along an edge for ages when of course a line that's five units long needs to span *six* cells if it's to begin and end in cell centres.

Got there in the end, though, and it appears that I can look forward to a new BRB for my troubles

Joined: July 16th, 2017, 5:07 am
I made the same error as Sprout initially, forgetting that five units would have to span six cells. Since there could not be any ambiguity, determining the four points for the rhombus was surprisingly easy.

Very nice puzzle with an unusual theme. The final grid looked like one of those puzzles where you have to fit lots of shapes into a square or other geometrical figure.

Joined: July 16th, 2017, 8:51 am
"Area of rhombus is base times height. Base is 5 and height is 4. "

Quite. Exactly the same as a rectangle, of course. Unfortunately, I forgot to make sure the sides were equal and drew another parallelogram (ie a 5x 4 rectangle, effectively, slightly tilted to the right. I suppose I needed to measure the base and find where one side of that length would intersect the top, using a compass. It would I think have been unwise to rely on the answer being unambiguous. That was not clear and indeed, as it turned out, neither was it true. I can't get my head round how you'd draw one "diamond shaped" in relation to the grid squares, as shown on the solution. I wonder if anyone actually submitted either of those possibilities.

Joined: July 16th, 2017, 7:34 pm
No compass needed. The length of any sloping line connecting cell centres can be found using Pythagoras's theorem for right angle triangles. Hence the top rhombus has sloping line of length 5 because 5 is the square root of 3 squared plus 4 squared.

Joined: July 15th, 2017, 9:42 pm
I struggled for ages to get the rhombus in, because I interpreted "All items are formed of straight lines joining cell centres" to mean that the straight lines had to go through the centre of EVERY cell they passed through (as indeed they did in the other shapes). Of course, the instruction doesn't stipulate anything of the sort if read absolutely literally, and I wish I'd twigged that several hours earlier! Nice puzzle.

Joined: July 16th, 2017, 8:51 am
"No compass needed. The length of any sloping line connecting cell centres can be found using Pythagoras's theorem for right angle triangles. Hence the top rhombus has sloping line of length 5 because 5 is the square root of 3 squared plus 4 squared. "

I don't understand the term "sloping length of 5": I would have measured the length of the base (3.5cm on the online grid) then a 3.5cm-set compass-drawn arc takes you straight to the required place.