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I agree that either interpretation (the "layman's and", or using set theory) should in fairness be marked correct. However I find it hard to believe that Q created THAT almost-final grid without having set theory in mind.

@candledave I agree. We'll see in due course but to me A and B doesn't equal the intersection of A and B, it's all A and all B. The quote says 'and'.

It's been a while since I did the whole A u B n C' thing though. 😄

If can do all three consecutively then there must be a times when A alone, B alone and C alone are feasible.

Been working on this all week, and think I finally have a full grid, bar ambiguities. But now very stuck!

Can’t work out 22a - any hints?

And please can someone tell me what Pythagoras has to do with this? If I have the correct four word phrase, the shape is not a triangle. And even if it were, what are the units of measurement?

Unless the shapes intersect somehow and give the triangle?

adeano
pythagorean triples (wiki) will give you your unit

@smithsax It's a fair point, concurrent and consecutive could possibly give different results. I suspect Buddy is right in what the setter intends though and we are to assume A AND B isn't A+B...although we have to make assumptions on the exact universal set and individual set definitions. I look forward to the published result. 👍

@1Esk19

Sorry, don’t follow. I figured it was Pythagorean triples people were hinting at, but they don’t have units. The sides could be measured in mm or km or even furlongs!

Consider a right angled triangle of base 3 units and height 2 units. The length of the hypotenuse is the square root of 3square plus two square - the square root of 13.
Now consider the 4 extra words and you see it gives a precise dimension which will intersect at the corners of 8 such triangles. This means that it takes in only 20 squares.
The size of the units is irrelevant but in this case is the length of a cell.

It’s Pythagoras… but not Pythagorean triples.

If you haven’t parsed 22A, you may not yet have the correct phrase to describe the shape and dimensions.

As mentioned earlier, this phrase gives the precise dimensions (in units of one grid square) you need for the endgame.

Just to add my twopennorth on the shading, I originally did the bigger area, then read the thread and agreed the smaller area is more consistent with classic set theory.

But have now looked at the actual quote again and I think the quote leads you pretty unambiguously to the bigger area. He is clearly saying you can't have either without the B. But I suspect the smaller area will be marked correct. Will be interesting to see. I don't submit, so not sure what I'd go for if I did.