# Puzzling Adventures Main Puzzle Solution - September 2008

Solutions:

1. The lowest-energy way to go is to use:
a) The slowest speed on the lake (water speed = 5 kmh; energy = 6 kWh);
b) The slowest speed on the 18-km portion with a 2-kmh downstream current (water speed = 5 kmh, land speed = 3 kmh and energy = 6 kWh);
c) The fastest speed on the 24 km portion (water speed = 15 kmh, land speed = 8 kmh and energy = 15 kWh).

That plan would take 6 + 6 + 3 = 21 hours and would consume a total of 27 kWh.

2. One thing you could do is to go faster on the lake. If you go 10 kmh, you would save 3 hours and consume 3 more kWh. That is not the best thing you could do, however. You would do better if you increased your water speed to 15 kmh on the 18-km portion: doing so would increase your energy consumption by less than 0.93 kWh but decrease your time by 4.62 hours. That strategy would leave you a bit more than 2.0 kWh. You can use that energy only on the 30-km lake journey. Suppose that you go from a water speed of 5 kmh to 10 kmh after 4 hours. So, in the first 4 hours you travel 20 km. Then you travel the last 10 km in 1 hour. This would consume the 2 kWh you have left but save an additional hour. So, you can make the trip in about 21 - 5.6 = 15.4 hours on 30 kWh of energy.

### ABOUT THE AUTHOR(S)

Dennis Shasha is at the Courant Institute of Mathematical Sciences, New York University. His most recent puzzle book, Puzzles for Programmers and Pros, was published in 2007 by John Wiley and Sons/Wrox.

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1. 1. BenGraham 08:27 PM 9/3/08

6 + 6 + 3 = 15, last I checked. Not 21.

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2. 2. BenGraham 08:41 PM 9/3/08

Also, I find the following to be the most efficient use of the 30 kw battery:
15 km/h on the 24 km stretch: 3 hours, 15 kw
15 km/h on the 18 km stretch: 1.38 hours, 6.92 kw
10 km/h on the first 20 km of the lake: 2 hours, 6 kw
5 km/h on the remaining 10 km of the lake: 2 hours, 2 kw
Total consumption: 8.38 hours, 29.92 kw

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3. 3. andres100 11:59 AM 9/4/08

6+6+3=21 ??????????????

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4. 4. njroux in reply to 01:05 PM 9/11/08

My 11 year old says 6+6+3 = 15 not 21 as you say - please fix the answer to your River Run puzzle.

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5. 5. njroux 01:05 PM 9/11/08

My 11 year old says 6+6+3 = 15 not 21 as you say - please fix the answer to your River Run puzzle.

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