Thinking Mathematically Problem Solving

So sorry to have a trouble in posting the scanned solution for my problem .
Solution for the problem is here
Game of 31

Mental Solution Strategy & Descriptions

1+2+3+4+5 Sum of digits 1to5 is 15, so if player A

1+2+3+4+5 starts with 1 will win at the end with 31.

1= 31 so announcing 1 is the best option to win

2+3+4+5 Now to find the strategy ,If the first player

1+2+3+4+5=29 or chooses to start with 2 he can only win if

1+2=32 total changes ,either 2less or 1more than 31

3+4+5 yes, it works well. now if he starts with 3 1+2+3+4+5 then to win he needs a change in total either 1 =28 or 2+3=33 3 less or 2 more than 31

4+5+ 1+2+3+4+5+1+3=31 again I check if he starts with 4 he can win if total changes to 27 or 34 i.e either 4 less or 3 more than 31.

Question: what if numbers are 1,3,5then I have 1+3+5=9x3=27+4=31, simply three full 1+3+5+1+3+5+1+3+5+1+3=31 rounds with 1,3,5 and wins for total of 31.

Hypothesis

3+5+1+3+5+1+3+5+1=27 or +3+5=35 i.e if he wants to start with 3 then for

winning condition of total should be either

27 or 35.

hence it gives me only one fixed number to start for a fixed total if I reduce or increase the total then I can have another option for first number to announce.