Dudeney just gave one example namely \(981324576\) where the nine digits are so arranged that they form "four"
square numbers: \((9)(81)(324)(576)\) or \((3^2)(9^2)(18^2)(24^2)\).
Evidently the permutations of these four squares also result in ninedigitals.
Can you create the full list of all solutions ?

What about other than four squares? How many arrangements can you find that gives "five', "three" and "two" squares?
It is a similar challenge as with the four squares. It shouldn't be so difficult to squeak your program code in order
to find these e.g. "three" or "two" solutions as well.

"Now, can you put the nine digits all together so they form a "single" square number?" Dudeney asked.
The smallest possible and largest possible solutions are already studied and known. Follow this link to Topic 2.2
\((139854276)\) is \((11826^2)~~\) and \(~~(923187456)\) is \((30384^2)\)

And now it is time to delve into the many possible variations.
Change the 'squares' into 'primes', 'cubes' or 'higher powers'. Oh yes, what would be the largest power possible.
What about a mix of powers. What about doubling or tripling the digits of the ninedigitals and pandigitals...
Be as creative as possible to the best of your ability. Success!

The analogue challenge now with pandigitals. Provide the full listings.
Here are some examples to get you going.

Four squares→ \((4)(25)(81)(30976)\) is \((2^2)(5^2)(9^2)(176^2)\)

Three squares→ \((9)(81)(4730625)\) is \((3^2)(9^2)(2175^2)\)

Two squares→ \((7056)(321489)\) is \((84^2)(567^2)\)

One square → \((1026753849)\) is \((32043^2)~~\) and \(~~(9814072356)\) is \((99066^2)\)