I like Pete's alpha subset of P&M suggestion and as no one has made one, I will "break the ice."

Does anyone know where on Earth (if any where) a mass falling in vacuum from rest will drop exactly 1m in exactly 0.45 seconds?

A strange question, until you work out that at that point g (in MKS units) is:

9.876543210m/s^2 (not sure of the final zero as my cheap calculator does not give ten places.)

Which leads to the math questions:

(1) What is the probability of a two

(2) Does the answer to (1) depend upon the functional relationship? (I am almost sure the answer to this is “yes” so lets assume that the relationship is the one given by the physics of this “Where on Earth” is g = 9.876543210 m/(s^2) problem.)

(3) are the probabilities of (A) and (B) out puts equal? If not which is greater, and is there any fixed relationship between these different probabilities, INDEPENDENT OF THE FORM of the functional relationship linking them?

The original post 1's math part (two questions) were poorly stated questions. - Perhaps these three are still in need of help from a real mathematician. See Post 14 also for more discussion.

PS I also like that my not very important first alpha post as it mixes physics and math.

Does anyone know where on Earth (if any where) a mass falling in vacuum from rest will drop exactly 1m in exactly 0.45 seconds?

A strange question, until you work out that at that point g (in MKS units) is:

9.876543210m/s^2 (not sure of the final zero as my cheap calculator does not give ten places.)

Which leads to the math questions:

(1) What is the probability of a two

**consecutive**decimal digit “input” producing all ten decimals in consecutive order “output”? I.e. either (A) 9876543210 or (B) 0123456789, with the decimal placed anywhere among them. (I am almost sure the decimal location is just a “scaling factor” in the functional relationship between “input” and its “output” which could be eliminated to make either (A) and (B) be integers (no decimal point) with exactly unchanged probability for the answer.(2) Does the answer to (1) depend upon the functional relationship? (I am almost sure the answer to this is “yes” so lets assume that the relationship is the one given by the physics of this “Where on Earth” is g = 9.876543210 m/(s^2) problem.)

(3) are the probabilities of (A) and (B) out puts equal? If not which is greater, and is there any fixed relationship between these different probabilities, INDEPENDENT OF THE FORM of the functional relationship linking them?

The original post 1's math part (two questions) were poorly stated questions. - Perhaps these three are still in need of help from a real mathematician. See Post 14 also for more discussion.

PS I also like that my not very important first alpha post as it mixes physics and math.

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