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# some 5 minute brain teasers

Go to solution Solved by bonanova,

## Question

1. if all borks are grogs, and all grogs are snorts, are all snorts borks?

2. prove that GCD(A,B) = GCD(A+B,A) = GCD(A+B,B)

3. how much water, approximately, would you need to cover all land on earth in 3 feet of snow?

4. whats the shortest distance between any two points on a globe? A) straight line B) curved line

5. and just to be silly: what's the speed of dark?

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• Solution

1. No

2. Let  f = GCD (A, B) so that A = f a and B = f b where GCD (a, b) = 1.
Then (A+B) = f (a+b).
GCD (A+B, A) = f GCD (a+b, a) = f  = f GCD (a+b, b) = GCD (A+B, B) = GCD (A, B).

3. Approximately,
R ~ 4000 mi;
land area ~ (3/10)(4) pi R2 sq miles;
3' of snow ~ 3" of water = 3/(12x5280) miles of water.
Do the math: (land area) x (water depth) cubic miles of water would be needed..

4. It depends.
A) if "on a globe" refers just to the points then the distance between them is the length of a straight line;
B) if "on a globe" refers to the distance then the distance on the globe's surface is the length of a curved line.

5. The speed of light.

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