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

[HenHanna]

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?)

[Barry Schwarz]

Post by HenHanna
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.

[HenHanna]

Post by Barry Schwarz

Post by HenHanna
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.

[Peter Moylan]

Post by HenHanna

Post by HenHanna
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.

Post by HenHanna
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.

[HenHanna]

Post by Peter Moylan

Post by HenHanna
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.

Post by Peter Moylan

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 .....

[Barry Schwarz]

Post by HenHanna
-- 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.

[HenHanna]

Post by Barry Schwarz

Post by HenHanna
-- 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.

Post by Barry Schwarz
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) ?