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« All Eyes Are On The Fed Tomorrow | Main | Solution To The Canoe Riddle »

September 19, 2007

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Anne and Bill cross first (2 minutes).
Anne comes back for Sue. (1 minute)
Anne and Sue cross next. (5 minutes)
Anne comes back for Mike. (1 minute)
Anne and Mike cross. (10 minutes)

Total time: 19 minutes

With Ann in the canoe for all crossings She can only paddle on the return trips, but that maximizes the total time with the two return trips only taking 1 minute each.

Ann+Bill out 2 min
Ann back 1 min
Ann+Sue out 5 min
Ann back 1 min
Ann+Mike out 10 min
Total 19 min

I'm afraid that maybe this is too simple a solution and I'm missing something!

Uggh... I was so wrong, there is a better solution!

A+B out 2
B back 2
M+S out 10
A back 1
A+B out 2
Total 17

The key is that it is inevitable that Mike must paddle at least one crossing (10 minutes). But, we were able to cancel out Sue's 5 minute time by having her cross with Mike!


Ann & Bill cross first, taking 2 minutes, and then Ann crosses back, adding 1 more minute. Then Sue and Mike cross together, taking 10 minutes. Bill comes back in the canoe, adding 2 minutes, and then Ann & Bill cross together again, for another 2 minutes. 17 minutes total. I think the key is to have Sue and Mike go at the same time.

Bill and Ann cross - 2 min.
Ann returns alone - 1 min.
Sue and Ann cross - 5 min.
Ann returns alone - 1 min.
Mike and Ann cross - 10 min.

Total 19 min.

Mike paddle sue Across and then Billpaddle Anne back to the other side... total 12 minutes.

I am sure there is more to it, but I can not seem to think it!

a. Bill rows Ann across
b. Bill rows back

c. Mike rows Sue across
d. Ann rows back

e. Bill rows Ann across

17 minutes total.

b and d are interchangeable.

OK - without looking to break or bend rules, or assume other 'facts not in evidence':

Mike & Ann go - Mike paddling (10 min)
Ann paddles back alone (1 minute)
Sue & Ann go - Sue paddling (5 minutes)
Ann paddles back alone (1 minute)
Ann & Bill go - Bill paddles (2 minutes)
19 minutes total.

There's room for pushing the rules here with respect to 'all must cross in the canoe' - to wit, all cross IN the canoe at least once, but perhaps they can drift along outside afterwards, if necessary? Or perhaps there is another way of sending the canoe back without a person in it - i.e., by running a line with the canoe (Mike & Sue in it - Mike paddling - 10 mins) and then the remaining people on shore pulling the canoe back with the rope and Bill & Ann crossing - another 2 minutes, for 12 minutes plus however long it takes to pull the canoe back over: probably a minute or less.

There's a lot of assumptions undealt with here, as well: i.e. define "crossing in" - does that mean in the canoe the whole time? Or can they take turns with differing people in the water at different times?

so - what clever solution do you have for us, showing how we've missed elegant freedom, by focusing on our constraints? [I just know I'm gonna be kicking myself!]

I think they can get everyone across in 19 minutes. Ann, the 1-minute paddler, always rides in the canoe. She crosses with Mike in 10 minutes, then returns by herself in 1 minute. (11 minutes) She then crosses with Sue in 5 minutes and returns by herself in 1 minute (6 minutes). She then crosses with Bill in 2 minutes, which puts all four on the other side of the lake in a total of 11+6+2=19 minutes.

Ann is always in the canoe. The slower ones paddle across and Ann paddles back really fast to get the next one. I think I counted 19 minutes.

I posed this riddle to my Logic class.

They were not allowed to look at the comments and they were only given 5 minutes to figure it out.

Below is their conclusion:
Mike and Anne go across first = 10 minutes
Anne returns alone = 1 minute
Anne picks up Bill = 2 minutes
Anne returns alone = 1 minute
Anne picks up Sue = 5 minutes

I didn't check the commments either - but - sounds to me like they have a pretty decent shot at having the right answer:)

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