• #### VIER and NEUN are 4-digit squares ---- (JFK's "myth)

From HenHanna@21:1/5 to All on Tue Jun 11 14:34:14 2024
XPost: sci.lang, alt.usage.english, sci.math

VIER and NEUN represent 4-digit squares, each letter denoting a
distinct digit. You are asked to find the value of each, given the
further requirement that each uniquely determines the other.

The "further requirement" means that of the numerous pairs of
answers, choose the one in which each number only appears once
in all of the pairs.

-------- Is this easy to understand?
(What the problem is asking?)

% Problem: VIER and NEUN are 4-digit squares; determine distinct V, I,
% E, R, N, and U, such that there is a unique solution (VIER,NEUN) for
% some particular E.

-------- Ok.. that makes more sense.

The great enemy of the truth is very often not the lie -- deliberate,
contrived and dishonest, but the myth, persistent, persuasive, and
unrealistic. Belief in myths allows the comfort of opinion without the discomfort of thought.
----- John F. Kennedy 35th president of US 1961-1963 (1917-1963)

like what kind of MYTH was he talking about?

(is this where M.Parenti got his notion?)

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• From Barry Schwarz@21:1/5 to All on Wed Jun 12 08:07:45 2024
XPost: sci.math

On Tue, 11 Jun 2024 14:34:14 -0700, HenHanna <HenHanna@devnull.tb>
wrote:

VIER and NEUN represent 4-digit squares, each letter denoting a
distinct digit. You are asked to find the value of each, given the
further requirement that each uniquely determines the other.

The "further requirement" means that of the numerous pairs of
answers, choose the one in which each number only appears once
in all of the pairs.

-------- Is this easy to understand?
(What the problem is asking?)

% Problem: VIER and NEUN are 4-digit squares; determine distinct V, I,
% E, R, N, and U, such that there is a unique solution (VIER,NEUN) for
% some particular E.

-------- Ok.. that makes more sense.

While there are 15 solutions for the six variables, only when E=4 is
the solution unique: 6241 and 9409.

While E=6 and E=5 both have multiple solutions, N=1 produces the only
other unique pair: 7569 and 1681.

E=5 has two solutions.

E=6 and N=4 has five solutions. E=6 and N=5 has six solutions.

--
Remove del for email

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• From HenHanna@21:1/5 to Barry Schwarz on Wed Jun 12 23:52:11 2024
XPost: sci.math, sci.lang, alt.usage.english

On 6/12/2024 8:07 AM, Barry Schwarz wrote:
On Tue, 11 Jun 2024 14:34:14 -0700, HenHanna <HenHanna@devnull.tb>
wrote:

VIER and NEUN represent 4-digit squares, each letter denoting a
distinct digit. You are asked to find the value of each, given the
further requirement that each uniquely determines the other.

The "further requirement" means that of the numerous pairs of
answers, choose the one in which each number only appears once
in all of the pairs.

-------- Is this easy to understand?
(What the problem is asking?)

% Problem: VIER and NEUN are 4-digit squares; determine distinct V, I,
% E, R, N, and U, such that there is a unique solution (VIER,NEUN) for
% some particular E.

-------- Ok.. that makes more sense.

While there are 15 solutions for the six variables, only when E=4 is
the solution unique: 6241 and 9409.

While E=6 and E=5 both have multiple solutions, N=1 produces the only
other unique pair: 7569 and 1681.

E=5 has two solutions.

E=6 and N=4 has five solutions. E=6 and N=5 has six solutions.

i've been wondering... This was a nice exercise in Python programming,

but can a (average) human solver comfortably enjoy solving it?

NEUN is a 4-digit square, so N can be 1, 4, 5, 6, or 9.

then i'm stuck...

The next step would be: i'd have to use a Calculator to
get the list of 5 possibilities for NEUN.

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• From Peter Moylan@21:1/5 to HenHanna on Thu Jun 13 19:58:02 2024
XPost: sci.math, sci.lang, alt.usage.english

On 13/06/24 16:52, HenHanna wrote:
On 6/12/2024 8:07 AM, Barry Schwarz wrote:
On Tue, 11 Jun 2024 14:34:14 -0700, HenHanna <HenHanna@devnull.tb>
wrote:

VIER and NEUN represent 4-digit squares, each letter denoting a
distinct digit. You are asked to find the value of each, given the
further requirement that each uniquely determines the other.

The "further requirement" means that of the numerous pairs of
answers, choose the one in which each number only appears once
in all of the pairs.

-------- Is this easy to understand?
(What the problem is asking?)

The original problem statement is easy to understand. Your restatement
of the "further requirement" is hard to understand, and I suspect it's incorrect.

i've been wondering... This was a nice exercise in Python programming,

but can a (average) human solver comfortably enjoy solving it?

I would instinctively write a computer program to solve it. I suspect,
though, that I could solve it manually if I had in front of me a table
of squares of numbers from 1 to 99.

--
Peter Moylan peter@pmoylan.org http://www.pmoylan.org
Newcastle, NSW

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• From HenHanna@21:1/5 to Peter Moylan on Thu Jun 13 15:10:35 2024
XPost: sci.math, sci.lang, alt.usage.english

On 6/13/2024 2:58 AM, Peter Moylan wrote:
On 13/06/24 16:52, HenHanna wrote:
On 6/12/2024 8:07 AM, Barry Schwarz wrote:
On Tue, 11 Jun 2024 14:34:14 -0700, HenHanna <HenHanna@devnull.tb>
wrote:

VIER and NEUN represent 4-digit squares, each letter denoting a
distinct digit. You are asked to find the value of each, given the
further requirement that each uniquely determines the other.

The "further requirement" means that of the numerous pairs of
answers, choose the one in which each number only appears once
in all of the pairs.

-------- Is this easy to understand?
(What the problem is asking?)

The original problem statement is easy to understand. Your restatement
of the "further requirement" is hard to understand, and I suspect it's incorrect.

that (2nd paragraph) wasn't MY restatement.

i've been wondering...  This was a nice exercise in Python programming,

but can a (average) human solver comfortably enjoy solving it?

I would instinctively write a computer program to solve it. I suspect, though, that I could solve it manually if I had in front of me a table
of squares of numbers from 1 to 99.

it turns out that...

-- there are only 68 4-digit squares

--- i'd have expected 300 or more.
but ok... Sqrt(10000) is 100

-- The only 4-digit squares with the [X..X] pattern
are
['1521', '1681', '4624', '5625', '9409']

(only 5 of them)

-- Can a square (number) be palindromic?

Other than 121, 12321, 1234321 .....

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• From Barry Schwarz@21:1/5 to All on Thu Jun 13 18:41:15 2024
XPost: sci.math

On Thu, 13 Jun 2024 15:10:35 -0700, HenHanna <HenHanna@devnull.tb>
wrote:

-- Can a square (number) be palindromic?

Other than 121, 12321, 1234321 .....

Why are you posting this to sci.lang and alt.usage.english?

484, 676, 10201, 14641, 40804, 44944, 69696, 94249, 698896, 1002001, 637832238736 and a whole lot more.

--
Remove del for email

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• From HenHanna@21:1/5 to Barry Schwarz on Fri Jun 14 01:56:36 2024
XPost: sci.math

Barry Schwarz wrote:

On Thu, 13 Jun 2024 15:10:35 -0700, HenHanna <HenHanna@devnull.tb>
wrote:

-- Can a square (number) be palindromic?

Other than 121, 12321, 1234321 .....

Why are you posting this to sci.lang and alt.usage.english?

because (for one thing)
palindromes are bigger (more important) in natural
languages.

484, 676, 10201, 14641, 40804, 44944, 69696, 94249, 698896, 1002001,
637832238736 and a whole lot more.

thanks.

Is there something interesting about palindromic Numbers?

Do palindromic squares follow a pattern (or patterns) ?

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