From Newsgroup: rec.puzzles

From Martin Gardner's book 'Sphere Packing, Lewis Carroll, and Reversi'.

The Square Root of Wonderful was the name of a recent play on Broadway.
If each letter in WONDERFUL stands for a different digit (zero excluded)
and if OODDF, using the same code, represents the square root, then what
is the square root of wonderful?

Of this problem Gardner says (paraphrased by me, as the original
referred to two problems): "This problem seems to call for a digital
computer so that hundreds of combinations of digits can be tested in a reasonable length of time. However, if approached properly and with the
aid of a clever dodge or two, the problem can be solved with very little pencil and paper work".

Feel free to say which method you employed.
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From Newsgroup: rec.puzzles


David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> posted:

From Martin Gardner's book 'Sphere Packing, Lewis Carroll, and Reversi'.

The Square Root of Wonderful was the name of a recent play on Broadway.
If each letter in WONDERFUL stands for a different digit (zero excluded)
and if OODDF, using the same code, represents the square root, then what
is the square root of wonderful?
. . .
Feel free to say which method you employed.

I solved it by hand. OO+ x OO+ = WOx+ has only one solution, and there
are then only two choices for D. The fact that FxF rea F and FxF rea xF reduces us to only four cases, which I checked individually.

Cheers,
James
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From Newsgroup: rec.puzzles

James Dow Allen <user4353@newsgrouper.org.invalid> writes:

David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> posted:

From Martin Gardner's book 'Sphere Packing, Lewis Carroll, and Reversi'.

The Square Root of Wonderful was the name of a recent play on Broadway.
If each letter in WONDERFUL stands for a different digit (zero excluded)
and if OODDF, using the same code, represents the square root, then what
is the square root of wonderful?
. . .
Feel free to say which method you employed.

I solved it by hand. OO+ x OO+ = WOx+ has only one solution, and there
are then only two choices for D. The fact that FxF rea F and FxF rea xF reduces us to only four cases, which I checked individually.

Pretty similar, but in my head I only managed to restrict it to five cases:

phil@dovespaz:/tmp$ for i in 3 4 7 9; do echo $i $(((22880+$i)**2)); done | grep ^.....8
7 523814769

phil@dovespaz:/tmp$ for i in 4; do echo $i $(((22990+$i)**2)); done | grep ^.....9

Which one was I failing to reject?

ObPuzzle:
Solve whichever one of these is verbally more appealing (they're the
same puzzle):
ARCHDUKES = DUDES^2
INCUBATES = BABES^2
And there's plenty more where that came from...

Phil
--
We are no longer hunters and nomads. No longer awed and frightened, as we have gained some understanding of the world in which we live. As such, we can cast aside childish remnants from the dawn of our civilization.
-- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/
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From Newsgroup: rec.puzzles

In article <87plbnswts.fsf@asdf.ee>, Phil Carmody <pc+usenet@asdf.org> wrote:

If each letter in WONDERFUL stands for a different digit (zero excluded)

phil@dovespaz:/tmp$ for i in 3 4 7 9; do echo $i $(((22880+$i)**2));
done | grep ^.....8

If the digits of WONDERFUL are all different, and none of them zero,
they add up to 45 so it and its square root must be multiples of 3.

-- Richard
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From Newsgroup: rec.puzzles

richard@cogsci.ed.ac.uk (Richard Tobin) writes:

In article <87plbnswts.fsf@asdf.ee>, Phil Carmody <pc+usenet@asdf.org> wrote:

If each letter in WONDERFUL stands for a different digit (zero excluded)

phil@dovespaz:/tmp$ for i in 3 4 7 9; do echo $i $(((22880+$i)**2));
done | grep ^.....8

If the digits of WONDERFUL are all different, and none of them zero,
they add up to 45 so it and its square root must be multiples of 3.

Very smart! So only 2 cases needed full checking, both for the D=8 case,
and none for the D=9 case!

Cheers,
Phil
--
We are no longer hunters and nomads. No longer awed and frightened, as we have gained some understanding of the world in which we live. As such, we can cast aside childish remnants from the dawn of our civilization.
-- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/
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From Newsgroup: rec.puzzles

It happens that David Entwistle formulated :

From Martin Gardner's book 'Sphere Packing, Lewis Carroll, and Reversi'.

The Square Root of Wonderful was the name of a recent play on Broadway. If each letter in WONDERFUL stands for a different digit (zero excluded) and if OODDF, using the same code, represents the square root, then what is the square root of wonderful?

I remember several of these games on the magazine "Sapere" (Knowledge), published in Italy in the 50-60 of past millennium, collected by my
father.
Unfortunately he dismissed all the boxes where he kept them for fifty
years, including several publications of "Selection from Reader's
Digest"... :'(

what a pity... if only he told me about this, I have enough room at
home to preserve those publications.
--
/-\ /\/\ /\/\ /-\ /\/\ /\/\ /-\ T /-\
-=- -=- -=- -=- -=- -=- -=- -=- - -=-
........... [ al lavoro ] ...........
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From Newsgroup: rec.puzzles

On 19/09/2025 09:24, Ammammata wrote:

I remember several of these games on the magazine "Sapere" (Knowledge), published in Italy in the 50-60 of past millennium, collected by my father. Unfortunately he dismissed all the boxes where he kept them for fifty
years, including several publications of "Selection from Reader's
Digest"... :'(

what a pity... if only he told me about this, I have enough room at home
to preserve those publications.

That is a pity. There are some copies of this publication available on-line.

https://archive.org/details/Sapere

I'll post a question from Issue 64 which concentrates on the work of
Marconi.
--
David Entwistle
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