River crossers

Posted by: CanukDenis

River crossers - 03/27/13 09:18 AM

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?
Posted by: CCbomber

Re: River crossers - 03/28/13 01:16 AM

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
Posted by: CanukDenis

Re: River crossers - 03/28/13 07:44 AM

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.