River crossers

26 guys (named A to Z!) have to cross a river.

Only one canoe is available, and it can take at most 2 guys.

A is the fastest: takes him 1 second to row across (told you he was fast!).

Then we have B:2 seconds, C:3 seconds and so on to Y:25 seconds, Z:26 seconds.

When 2 guys are crossing, the slowest one rows (Why? To make this puzzle harder!)

What is shortest possible time to get all 26 guys across?

242 sec? (not counting any time on shore)

A,B cross, A returns, 3 sec
C,D cross, B returns, 6 sec
A,B cross, A returns, 3 sec
E,F cross, B returns, 8 sec
A,B cross, A returns, 3 sec
G,H cross, B returns, 10 sec
.
.
.
W,X cross, B returns, 26 sec
A,B cross, A returns, 3 sec
Y,Z cross, B returns, 28 sec
A,B cross................, 2 sec

Total time = 242 sec

Correct.

Notice the "6 + 8 + 10 + ... + 28" series, and the "3 sec" return trips.

n = (number of crossers + 2) / 2

time = n(n+1)-6 +3(n-2) + 2 = n^2 + 4n - 10

Can be rearranged as a direct function of c (number of crossers):
time = (c^2 + 12c - 20) / 4

Slightly different if odd number of crossers.