When I first saw this, I was surprised that the answer is independent of the starting circumference. It's interesting that the answer is surprising, since I'm not surprised that circumference is proportional to radius. Maybe that means that the distributive property of multiplication is nonintuitive. I doubt the explanation is that simple, since another form of the question doesn't seem to be a riddle at all: A company pays each of its employees $6.28 per hour, for a total of $40,000 per hour. How much more would the company need to spend per hour to hire one more employee?
C = 2*pi*R
R' = R+1
C' = 2*pi*(R+1) = 2*pi*R + 2*pi = C + 2*pi
Paul

If string is lifted 1m, effective diameter increases by 2m. let d = 2meters. If D is original diameter then difference in circumference is
C = (Pi*(D+d) - Pi*D) = Pi*d = 2*Pi meters = 6.283 meters

If we assume a perfect circle of string then we can calculate the Diameter D
C=Pi x D
D=C/Pi = 40x10^6/Pi
When you lift the string by 1 Meter, the diameter increases by 2 Meters.
Then all you need to do is calculate the new circumference C and take the difference between old and new.
NewC=(C/Pi + 2) x Pi
To get the difference:
Difference = NewC ? C
= [(C/Pi + 2) x Pi ] ? C.
= C + 2xPi ? C = 2xPi
The answer I get is 2xPi
Rick.

It would be interresting how this equation looks, which gives the result how far we have to move to north or south...
A real topic for my math teacher, who teased me with such questions back in school some decades ago.

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