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August 29, 2008

Crossing The Lake Puzzle

There are four people in an adventure race that
need to get across a lake. They have a small
canoe. The rules say that only the slowest person
in the canoe can paddle, only one or two can be
in the canoe at a time, and they must all cross
in the canoe. From practice, they know that:

Ann can paddle across in 1 minute.

Bill can paddle across in 2 minutes.

Sue can paddle across in 5 minutes.

Mike can paddle across in 10 minutes.

How do they get everyone across the river
in the fastest time without breaking
the rules?


Anonymous said...

17 minutes

Anonymous said...


ann bill -> 2
ann <- 1
ann sue -> 5
ann <- 1
ann mike -> 10

Secret Squïrrel said...

believe it or not, the first answer (17 min) is correct.

The trick is to not have Sue and Mike paddle across separately since that's already 15 min. Five trips are required (3 "forward" and 2 return). Mike & Sue can't be the first or last trip over because then Sue (or Mike) would have to also make a return journey (trip 2 or 4).

Ann + Bill -> 2 min
Ann <- 1
Sue + Mike -> 10
Bill <- 2
Ann + Bill -> 2

atkas said...

simply answer is change the canoe ...means exchange each other canoe and do it.

i guess so

Anonymous said...

16 minutes! from Jono at HRV.
First Criticism: Are we crossing a Lake or a River? two different parts. in any case we have two sides. Here is my 'thinking outside of the square' answer.

get everyone across the river in the fastest time without breaking the rules. (Assuming they all start on the same side)

Sue + Ann -> 5
<- 1 Anne

Ann has gone across the river in the canoe twice already so has satisfied the rules and gives the canoe to the guys.

Bill Mike -> 10

Everyone has followed the rules and is across the river in the fastest time, just not all on the same side.

This makes the fastest time 16 Minutes!

We can get down to 12 minutes if we think further outside the square and remove the assumption of them starting on the same sides, and have Mike & Sue on one side and Bill and Anne on the other.

I like my first answer(16), as my thinking is just a little bit outside the square and just beats the expected answer of 17. The second answer(12) is thinking too far out side the circle ;-)