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Why does Solve give me no solutions for this in Version 8.0.1?

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  Why does Solve give me no solutions for this in Version 8.0.1? Phil J Taylor <xptaylor@gmail.com> - 2011-07-01 00:42 +0000
    Re: Why does Solve give me no solutions for this in Version 8.0.1? Peter Breitfeld <phbrf@t-online.de> - 2011-07-02 09:04 +0000

#3423 — Why does Solve give me no solutions for this in Version 8.0.1?

This system of equations for the Magic Hexagon is indeterminate.
 Solve still provides useful information in  Version 6.0

ClearAll[a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s];
eqns = {
   a + b + c + d + e + f + g + h + i + j + k + l + m + n + o + p + q + r + s
- 190 == 0,
   a + b + c - 38 == 0,
   a + d + h - 38 == 0,
   a + e + j + o + s - 38 == 0,
   b + e + i + m - 38 == 0,
   b + f + k + p - 38 == 0,
   c + f + j + n + q - 38 == 0,
   c + g + l - 38 == 0,
   d + e + f + g - 38 == 0,
   d + i + n + r - 38 == 0,
   g + k + o + r - 38 == 0,
   h + i + j + k + l - 38 == 0,
   h + m + q - 38 == 0,
   l + p + s - 38 == 0,
   m + n + o + p - 38 == 0,
   q + r + s - 38 == 0
   };

Join[
 Solve[eqns, b], Solve[eqns, d], Solve[eqns, g],
 Solve[eqns, m], Solve[eqns, p], Solve[eqns, j],
 Solve[eqns, r], Solve[eqns, e], Solve[eqns, f],
 Solve[eqns, i], Solve[eqns, k], Solve[eqns, n],
 Solve[eqns, o], Solve[eqns, a], Solve[eqns, c],
 Solve[eqns, h], Solve[eqns, l], Solve[eqns, q],
 Solve[eqns, s]]

Out[1]: {{b -> j + n + o}, {d -> j + k + o}, {g -> i + j + n},
 {m -> f + j + k}, {p -> e + i + j}, {j -> -38 + d + g + r},
 {r -> -38 + h + l + m + p}, {e -> -38 + h + k + q + r},
 {f -> -38 + i + l + r + s}, {i -> -38 + f + p + q + s},
 {k -> -38 + e + m + q + s}, {n -> -38 + g + h + k + l},
 {o -> -38 + d + h + i + l}, {a -> -38 + i + m + n + q + r},
 {c -> -38 + k + o + p + r + s}, {h -> -38 + n + o + p + r + s},
 {l -> -38 + m + n + o + q +  r}, {q -> -38 + g + k + l + o + p},
 {s -> -38 + d + h + i + m +  n}}

Version 8.0.1 returns {}.

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#3450

Phil J Taylor wrote:

> This system of equations for the Magic Hexagon is indeterminate.
>  Solve still provides useful information in  Version 6.0
>
> ClearAll[a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s];
> eqns = {
>    a + b + c + d + e + f + g + h + i + j + k + l + m + n + o + p + q + r + s
> - 190 == 0,
>    a + b + c - 38 == 0,
>    a + d + h - 38 == 0,
>    a + e + j + o + s - 38 == 0,
>    b + e + i + m - 38 == 0,
>    b + f + k + p - 38 == 0,
>    c + f + j + n + q - 38 == 0,
>    c + g + l - 38 == 0,
>    d + e + f + g - 38 == 0,
>    d + i + n + r - 38 == 0,
>    g + k + o + r - 38 == 0,
>    h + i + j + k + l - 38 == 0,
>    h + m + q - 38 == 0,
>    l + p + s - 38 == 0,
>    m + n + o + p - 38 == 0,
>    q + r + s - 38 == 0
>    };
>
> Join[
>  Solve[eqns, b], Solve[eqns, d], Solve[eqns, g],
>  Solve[eqns, m], Solve[eqns, p], Solve[eqns, j],
>  Solve[eqns, r], Solve[eqns, e], Solve[eqns, f],
>  Solve[eqns, i], Solve[eqns, k], Solve[eqns, n],
>  Solve[eqns, o], Solve[eqns, a], Solve[eqns, c],
>  Solve[eqns, h], Solve[eqns, l], Solve[eqns, q],
>  Solve[eqns, s]]
>
> Out[1]: {{b -> j + n + o}, {d -> j + k + o}, {g -> i + j + n},
>  {m -> f + j + k}, {p -> e + i + j}, {j -> -38 + d + g + r},
>  {r -> -38 + h + l + m + p}, {e -> -38 + h + k + q + r},
>  {f -> -38 + i + l + r + s}, {i -> -38 + f + p + q + s},
>  {k -> -38 + e + m + q + s}, {n -> -38 + g + h + k + l},
>  {o -> -38 + d + h + i + l}, {a -> -38 + i + m + n + q + r},
>  {c -> -38 + k + o + p + r + s}, {h -> -38 + n + o + p + r + s},
>  {l -> -38 + m + n + o + q +  r}, {q -> -38 + g + k + l + o + p},
>  {s -> -38 + d + h + i + m +  n}}
>
> Version 8.0.1 returns {}.

You can get back the behaviour of Solve (v.6), setting the Option
Method, which in 8.0.1 defaults to Automatic:

SetOptions[Solve,Method->"Legacy"]

Now Solve will give you the expected results.

-- 
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

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