let's start with the last to clues and make a list of all 3-digit square numbers (and by making I mean just looking it up. it would be possible, but it's faster and lazier)
100
121
144
169
196
225
256
289
324
361
400
441
484
529
576
625
676
729
784
841
900
961
(source: https://math.tools/table/square-numbers-list
but I had to copy by hand...)
now let's eliminate all numbers from the list that don't have 13 as the sum of their digits and just keep the few that will remain.
256
625
841
now that's pretty much narrowing it down already, now let's test for the first two clues (I would have no idea how to start with these so I switched the order to make it doable)
The SECOND and THIRD digits make a 2-digit number
The FIRST number is a FACTOR of the 2-digit number
only 256 works, 2 is a factor of 6, but that wouldn't word for the other candidates. so 256 is the number we are looking for.
summing up the second and the third digit (I guess summing up the digits was meant here) also works for 256, if we wanna see a two-digit number as a result.
the key part here was to ignore the order the clues where listed I guess. much easier with just 3 possible numbers.
