From Newsgroup: rec.puzzles

From '536 Puzzles and Curious Problems' by Henry Ernest Dudeney.

Can you find two three-figure square numbers (no zeros) that, when put together, will form a six-figure square number? Thus 324 and 900 (the
squares of 18 and 30) make 324,900, the square of 570, only there it
happens there are two zeros. There is only one answer.

Note: by 'put together' Dudeney refers to concatenating the digits.
--
David Entwistle
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From Newsgroup: rec.puzzles

On 14/12/2025 13:06, David Entwistle wrote:

From '536 Puzzles and Curious Problems' by Henry Ernest Dudeney.

Can you find two three-figure square numbers (no zeros) that, when put together, will form a six-figure square number? Thus 324 and 900 (the
squares of 18 and 30) make 324,900, the square of 570, only there it
happens there are two zeros. There is only one answer.

Note: by 'put together' Dudeney refers to concatenating the digits.

....................................solution follows ....................................solution follow ....................................solution follo ....................................solution foll ....................................solution fol ....................................solution fo ....................................solution f ....................................solution ....................................solution ....................................solutio ....................................soluti ....................................solut ....................................solu ....................................sol
....................................so
....................................s
....................................
...................................
..................................
.................................
................................
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................
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.......
......
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....
...
..
.


I make it

15 * 15 = 225
25 * 25 = 625
475 * 475 = 225625
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within
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From Newsgroup: rec.puzzles


Richard Heathfield <rjh@cpax.org.uk> posted:

On 14/12/2025 13:06, David Entwistle wrote:

From '536 Puzzles and Curious Problems' by Henry Ernest Dudeney.

Can you find two three-figure square numbers (no zeros) that, when put together, will form a six-figure square number? Thus 324 and 900 (the squares of 18 and 30) make 324,900, the square of 570, only there it happens there are two zeros. There is only one answer.

Note: by 'put together' Dudeney refers to concatenating the digits.

...................................solution follows ...................................solution follow ...................................solution follo ...................................solution foll ...................................solution fol ...................................solution fo ...................................solution f ...................................solution ...................................solution ...................................solutio ...................................soluti ...................................solut ...................................solu ...................................sol
...................................so
...................................s
...................................
..................................
.................................
................................
...............................
..............................
.............................
............................
...........................
..........................
.........................
........................
.......................
......................
.....................
....................
...................
..................
.................
................
...............
..............
.............
............
...........
..........
.........
........
.......
......
.....
....
...
..
.
.

I make it

15 * 15 = 225
25 * 25 = 625
475 * 475 = 225625

how did you find them?


______________________

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From Newsgroup: rec.puzzles

On Sun, 14 Dec 2025 13:06:41 -0000 (UTC), David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> wrote:

From '536 Puzzles and Curious Problems' by Henry Ernest Dudeney.

Can you find two three-figure square numbers (no zeros) that, when put >together, will form a six-figure square number? Thus 324 and 900 (the >squares of 18 and 30) make 324,900, the square of 570, only there it
happens there are two zeros. There is only one answer.

Note: by 'put together' Dudeney refers to concatenating the digits.

I have a related puzzle -- one that I stumbled across by chance.
I will post it separately, but as it is somewhat related to this
puzzle, this post is a kind of a link.
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