Squares

[cinelli]

This puzzle is to find all numbers between 1000 and 2300 each of which is

. the product of three squares (>1) and
. the sum of whose digits is also a square.

Happy new year to all readers.

Cinelli

[9873210]

There are of course two ways to solve the puzzle.
The easiest is to note that the product of squares is also a square and do an exhaustive search on the 16 squares between 1000 and 2300. Of these only 1521, 1681 and 2025 have digits that sum to a square and only 2025 has enough prime factors to be the product of three non-trivial squares.

The harder way, because it requires much more background, can be represented by the excel formula "=year(today())"

Happy New Year.

[cinelli]

Well solved 9873210. That didn't take long.

Yes, the year 2025 is a perfect square and few will have seen one before. And it is unlikely that anyone here will live to see another. The fact that we are living in a square year even got a mention on the Today programme this morning.

Cinelli

[UncleEbenezer]

Yes, the year 2025 is a perfect square and few will have seen one before.

On the contrary, users of non-Roman calendars may well have done. For example, if my sources are correct our Jewish friends saw one just nine years ago.