Solution by DS8.

This was DS8's "train of thought":-

He first listed out the info up to #23 and saw the pattern which was:

No. of people <=> Best Seat
1 <=> 1
2 <=> 1
3 <=> 3
4 <=> 1
5 <=> 3
6 <=> 5
7 <=> 7
8 <=> 1
9 <=> 3
10 <=> 5
11 <=> 7
12 <=> 9
13 <=> 11
14 <=> 13
15 <=> 15
16 <=> 1
17 <=> 3
18 <=> 5
19 <=> 7
20 <=> 9
21 <=> 11
22 <=> 13
23 <=> 15
: :
: :


He noticed that when the # of pple is 4, 8 16 .... the best seat would be 1 (the first seat). He then associated them with the power of 2s.

He also noticed that the increment for each cycle is by 2. Eg. [1] [1,3] [1,3,5,7] [1,3,5,7,9,11,13,15 ....] This is the part when he thought that there should be a {times 2} in his formula.

Since he didn't know how to "write out" a formula, I told him to describe to me. He started with :-

1) "Find the difference between the no. of pple (n) and the closest power of 2 which is less than n"

2) Then multiply by 2

3) Add 1 (this "1" according to him is to add back the 1st seat)

After making him explained to me like 100x , he wrote down the formula... (He can't wait to go play his lego!)

1+(n-2^) x 2
(where the power of 2 is denoted by 2^)