Hi Mike,
That’s not the way my logic works out. But I might be wrong.
Let’s see what others have to say. Then i’ll outline my logic.
Betty is saying the truth when saying Grace lies.
Grace lies when saying that Ruth tells lies. So Ruth is telling the truth.
And then it falls over I see.
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Grace tells the truth that Ruth lies. Ruth lies that Betty and Grace lie, Betty lies, Grace doesn’t. Betty lies that Grace lies, but Grace tells the truth.
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I think this is true.
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Nicely explained Mike.
Both of your posts together, create a really good explanation of how to arrive at the logical conclusion that is consistent…
And it seems that Mulberry endorses your conclusion as well…
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3
Hmmm…
Let’s see what others have to say first 
For the avoidance of doubt, “rotate” and “revolve” have the same meaning.
How about 4 times? 3 times because of the ratios of the circumstances, plus 1 for the centre point of the small circle revolving aound the big one?
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It’s late here, but I think this is good.
In BC it could be a “bunch” of sand …
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Of course, that’s good 
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It’s surprising (to me) but true, that rolling one circle around another, Is different from rolling that same circle along the “flat” line generated by “cutting” and straightening out the second circle.
Well done Dozey.
And to Mike who gave it a shot…it appeared in a school exam question with multiple choice answers. The exam board was embarrassed because they didn’t include the correct answer. Even they thought the answer was 3 ! Seems like you are in good company
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Thanks Don, that was a really good tease
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Thank you Annalogg, glad you enjoyed it.
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A Pile or a Heap…
A pile of potatoes weighs 100kg and is put outside in the sun. 99% of the weight of these potatoes is made up of water. After a day in the sun, some of that water has evaporated such that only 98% of the weight of the potatoes is now made up of water.
What is the new weight of this pile of potatoes ?
My tired brain says 50kg. The non–water part of the potatoes has a weight of 1kg (1% of 100kg). This part hasn’t changed its weight, but the kilogram now accounts for 2% of the total weight. This leads to each percent now weighing 500g -> 100 * 500g = 50.000g or 50 kg.
Your tired old brain seems to be in perfect working order mulberry !
Well done !
This next one is plain and simple. But have a guess at the answer and then decide whether you are surprised at the answer when you’ve done the maths !
We had a street party last year. The distance between the two lampposts in our avenue is 100m. Mrs D created the bunting rope complete with flags and made it 101m long. We pinned one end of the bunting rope to the bottom of one lamppost and the other end to the base of t’other lamppost.
I raised the midpoint of the bunting on a post to form two sloping lines of bunting. It was very colourful. There was no slack in the rope and the bunting didn’t sag.
How high was my post ?
A lot higher than I thought it was going to be!