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I agree, emcee, yet another very unsatisfactory endgame. The setter appears to have set us a trap, but whether we choose to highlight ONE or TWO, either result is unsatisfactory in some way or other. I don't object to traps in principle, but given two alternatives, the intended solution should be clearly and demonstrably better than the other. I don't think that is the case here.

Not an enjoyable dilemma. I suspect only one solution is going to be allowable, unlike with the Italian translations a few weeks ago. The wrong option could easily have been removed after careful editing.

ONE looks neater for the highlighting symmetry.

Agree entirely

With apologies for over-posting, I have just realised that TWO also leaves the formula for circumference, so in all we would have:

Diameter – radius two (same as 2R)
Area – two pi radius squared
Circumference – two pi radius

I need to go back to school!

Area = pi radius squared

I think "Radius ONE" has to be the intended solution, for the reason that a) it preserves symmetry and b) if you go for radiustwo instead then the resulting highlighting about the circumference is wrong -- the area is then not pi but pi *r^2. This only gives pi exactly if the radius is one.

Annoying that the second option exists, and in particular as swain -> stain, word -> told, mortify -> mollify and tamest -> lamest is an easy fix one wonders if it was after all a deliberate thing to muddy the waters. But the highlighting surely indicates that RADIUS ONE lying along the diameter is the correct choice. This also strengthens the case for having AREA in the highlighting, as "(if the) RADIUS (of a circle is) ONE (unit, then the) AREA (is) 3.1415... (units^2)" is a correct statement.

Oh well. Another Listener with an unfortunate red herring/ ambiguity. Have been a few too many of them this year so far, although this one feels closer to solvers overthinking things than genuinely careless setting.

Jim360, how do you see "Radius one" = diameter?

With TWO highlighted we would have 'AREA and PI RADIUS SQUARED' highlighted in 37 cells - I don't see why you say that would be wrong.

It's surely enough that "radius one" is along a diameter, which struck me as what the preamble and the misprint corrections are getting at. A description of "diameter [is] inside a circle" seems to hint that you should highlight a circular string of letters and one of the diameters lying inside the circle.

For the second interpretation there is some level of jumping around to make the quote flow seamlessly, as the point where Pi finishes is nowhere near where "radius two" starts. And then in that interpretation the whole diameter bit disappears entirely. Radius two is no way to write diameter, and radius squared is not equal to the diameter, and nothing has been highlighted to make a diameter.

It's unfortunate that the "two" has appeared to muddy the waters, but I think it's a distraction rather than the actual solution.

‘It's surely enough that "radius one" is along a diameter’. You set puzzles I believe, Jim360, (as do I) and I can’t imagine that you would use the message given by the clues to mean highlight the diameter. The message (to me at least) implies that we are to ‘find’ the diameter in the circle – we all know where a diameter is. Diameter is 2R, and I agree isn’t normally written R2, but wouldn’t be wrong, particularly where one is trying to make the TWO do double duty. I grant you that it is not clear cut, and I don’t really like how TWO would be doing double duty for R2 and R squared, but I think that it is doing just that so that we see all the relevant formulas (or illustrate a relationship as described in the preamble) – area, circumference and diameter, they would all be there. I grant you that it involves a bit of ‘jumping around’, but I like better than what you are suggesting.

It is interesting that you mention in an earlier post that we might be overthinking things, when that is exactly what I thought when you brought the bit about ‘If the radius is one then…’. I am of the view that we are looking at formulas that we have had imprinted on our brains and not some maths sum.

Actual with further apologies to everyone, I think that I have just change my mind altogether. I will get my coat!