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November 14, 2009


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This little puzzle is from "Mathematics for the Nonmathematician" by Morris Kline,Dover Books,1967; originally involved water(and US pints),but I modified it for gathering sand.

A man goes to a sand pile with two jars, one holding 3 liters and the other 5 liters. How can he bring back exactly 4 liters?

I can provide the answer on a follow up comment

Excellent - Sand Puzzle #2! I'll leave it up for a while for readers to exercise their neurons over and then we'll see how many solutions we get. I have one, but I'm sure there are several, and the challenge then becomes doing it in the smallest number of steps.


I guess now it about past time to finish up the sand puzzle!:

The man fills the 5 liter jar and then fills the 3 liter jar from the 5 liter one. He empties the 3 liter jar and then pours the remaining 2 liters into the 3 liter jar. He now fills the 5 liter jar again with sand and pours enough to fill the 3 liter. Since there were 2 liters in the 3 liter jar and 1 liter is drawn down from the 5 liter jar, that leaves 4 liters in the it

There was another other way that I thought of by using the jars(if made of clear glass) as measuring cups by marking off the 5 liter level jar with the 3 liter level and 2 liters level on the 3 liter jar with "shifting sand" quantities betweeen them till I arrived at 4 liters.


A little late off the mark, but here are my solutions to the two sand puzzles (I guess you can withhold this comment until you're ready to reveal the answers):

Puzzle No. 1
1) Start both timers.
2) Elapsed time 7 min: Small timer is empty, big timer has 4 min of sand left. Flip the small timer.
3) Elapsed time 11 min: Big timer is empty, small timer has 3 min of sand left. Flip the small timer.
4) Elapsed time 15 min when the small timer is empty.

Puzzle No. 2
1) Fill the 5L jar.
2) Fill the 3L jar from the 5L jar, leaving 2L in the 5L jar.
3) Empty the 3L jar.
4) Empty the 5L jar into the 3L jar, which now has 2L of sand in it.
5) Fill the 5L jar again.
6) Fill the 3L jar from the 5L jar. This leaves 4L in the 5L jar.

P.S. Trivia: Puzzle No. 2 was used in one of the Bruce Willis "Die Hard" movies (the one in which Samuel L. Jackson co-starred).


Interesting way of solving maths problems. These days we rely far too much on calculators. If this method were to be taught in school, students would pay far more attention than when using traditional teaching ways. This method encourages us to use our brains instead of our fingers.

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