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Listener 4465; Got my knickers in a mobius twist  

Tweet Topic Started: Sep 15 2017, 05:17 PM (845 Views)  
Nick  Sep 15 2017, 05:17 PM Post #1 

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 Edited by Nick, Sep 15 2017, 05:24 PM.

Derek Harrison  Sep 15 2017, 06:15 PM Post #2 
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Luckily I seem to have got this puzzle right. It was a pleasure to see all the foursided figures in the grid. I was worried because I thought my rhombus covered more than 20 cells in the grid. Maybe someone can explain. 
John Reardon  Sep 15 2017, 09:58 PM Post #3 

The diagonals of the rhombus are 4√5 × 2√5 and its area is ½(4√5 × 2√5) = 20 
zax  Sep 16 2017, 08:52 AM Post #4 

Area of rhombus is base times height. Base is 5 and height is 4. 
Sprout  Sep 18 2017, 08:53 AM Post #5 

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 
Andy Stewart  Sep 20 2017, 12:32 PM Post #6 

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. 
Richard R  Sep 20 2017, 03:10 PM Post #7 

"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. 
zax  Sep 20 2017, 09:36 PM Post #8 

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. 
Alberich  Sep 21 2017, 09:14 AM Post #9 

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. 
Richard R  Sep 21 2017, 04:34 PM Post #10 

"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 3.5cmset compassdrawn arc takes you straight to the required place. 
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