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Crosswords and other puzzles

For discussion of all forms of mental gymnastics, especially that baffling final clue

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by Ingers - Wed 19th Oct 2005, 4:05pm
Ok, this is an old chestnut, but is the single one of these sorts of problems that took me the longest time (and led to at least 1 man-day's loss of productivity at Deloitte).

I think of 2 integers between 1 and 100. I tell Peter the Product and Simon the Sum.

1.) Peter: "I don't know what the numbers are"
2.) Simon: "I knew you wouldn't"
3.) Peter: "Now you've siad that, I do know"
4.) Simon: "Now you've said that I also know"

What are the numbers? No computer programmes allowed
by jpd - Wed 19th Oct 2005, 3:56pm
mjb said: OK, so I rushed the previous one a bit.

How aboot the centre of the earth, or is East undefined there as well. In which case, go out far enough such that your 1 mile East will take you back to where you started the Eastward leg.
East is definitely undefined along the whole of the straight line that runs through the North and the South pole. Also, how can you possibly walk at the centre of the Earth?

You are walking on the Earth's surface. And before you ask, no other form of transport is used.
by Mike - Wed 19th Oct 2005, 3:53pm
mjb said: How aboot the centre of the earth
Have you suddenly turned Canadian?
by mjb - Wed 19th Oct 2005, 3:51pm
jpd said: Where else could I be?
OK, so I rushed the previous one a bit.

How aboot the centre of the earth, or is East undefined there as well. In which case, go out far enough such that your 1 mile East will take you back to where you started the Eastward leg.
by jpd - Wed 19th Oct 2005, 3:41pm
Rich said: At a position one mile north of the place where walking east around the south pole brings you in a full circle 1 mile in circumference, back to the same point.
Is the right answer.

If we assume the small area around the South pole is flat, our start point would be any point on the circle which is 1 + 1 / (2 * pi) miles North of the South pole.

Where else could I be?
by Rich - Wed 19th Oct 2005, 3:38pm
jpd said: Also wrong.
Aw, come on! You start "on the equator", you finish "on the equator"!!

At a position one mile north of the place where walking east around the south pole brings you in a full circle 1 mile in circumference, back to the same point.
by jpd - Wed 19th Oct 2005, 3:36pm
Rich, using semantics said: On the equator?
Also wrong.
by Rich, using semantics - Wed 19th Oct 2005, 3:35pm
jpd said: Good. Where else could you be?
On the equator?
by jpd - Wed 19th Oct 2005, 3:34pm
mjb said: Also, depending on which north you take, you could be exactly 1 mile north of the South Pole.
Is also the wrong answer (East is undefined at the South pole).
by jpd - Wed 19th Oct 2005, 3:33pm
mjb said: Anywhere exactly 2 miles north of the South Pole.
Is the wrong answer.

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