3→7 +4

7→ 16 +9

16→65 +49

65→32 1 +256

Note that none of 1, 4, 9, 49, 256 are square numbers, that is, 1 2, 2 2, 3 2, 7 2, 16 2.

A rule was found: 3 was preceded by 2, so 2 2 was added.

7 is preceded by 3, so 3 2 is added.

16 is preceded by 7, so 7 2 is added.

65 is preceded by 16, so add 16 2.

So the last digit is 32 1+65 2 = 4546.

Induction:

To do this kind of problem, the first idea is to observe the change between two adjacent numbers.

Generally, we should look at the difference between addition and subtraction before looking at anything else. This problem combines addition and multiplication.

And be good at discovering laws.

Experience depends on accumulation, and this problem will naturally occur if you do too much.