Question

Earthworm, Centipede and Grasshopper

An earthworm weighing 50 g, a centipede weighing 30 g and a grasshopper weighing 20 g wish to cross the river.

They have one leaf at their disposal, which can carry< 60 g at most.

How do they cross the river?

 

Answer 1

The worm and the grasshopper set off on the leaf, with only half OF the worm on the leaf, the other half in the water.  If the specific gravity of the worm does not exceed 2.5 (which it surely does not), the buoyant force of the water on the submerged part of the worm will prevent the leaf from being overloaded.  Since worms can survive underwater for hours (if not days), this arrangement should be easy for the worm.  By flagellation of the submerged half, the worm can propel the leaf across the river. where the worm gets off.

The grasshopper then propels the leaf back to the starting side by kicking its jumping legs in the water.  It picks up the centipede and goes back to the far side by the same means

(The transfer could be made in one trip if the worm can tolerate being fully submerged while crossing, with the centipede holding onto the leaf and the submerged worm while the grasshopper paddles.)

Comments

Lol - your description and idea are outstanding, but this old puzzle did not include this eventuality (Hint: T. fährt ohne Begleitung).

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The old puzzle was far too simplistic, in only considering the masses of the creatures and the carrying capacity of the leaf.  It completely overlooked certain CRITICAL factors.   :-)

I suppose it expected the following solution:

1. Centipede and grasshopper cross over.
2. Either one returns.
3. Worm crosses over by itself, 'ohne Begleitung'.
4. The other creature on the far shore returns to the near shore.
5. Both the centipede and the grasshopper cross over to the far shore.

I think my solutions are much better for the following reasons:

1.  My solutions involve fewer (1 or 3, rather than 5) crossings.  This lowers the overall risk.  Besides, the leaf would probably become waterlogged and sink, if they tried to use it 5 times.

2. My solutions are better because, unlike the old puzzle, my solutions NEVER leave the  centipede alone with the worm at any time.  The carnivorous centipede, who would surely be hungry after his exertions, would eat the worm if the grasshopper were not there to intervene.   :-O

Oh, and here is another unorthodox 'ohne Begleitung' solution:   The centipede and the grasshopper cross over on the leaf, and the worm burrows through the earth under the river.  Again the risks are far lower than in the expected solution.

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Excellent ideas, Tink, and you found the correct solution for the "simplistic" old-fashioned version, reminding of La Fontaine et al. Congratulations!

Yes, I have also thought about the biological sides of these particular creatures (all of them represented by various "families", species and subspecies, all the more that they are from different "Phyla" - an annelid, an arthropod and an insect.

Even if the last idea is the most logical for nature, I am not sure if the rainworm can dig that deep, as the earth should not be too compact and there should be an intermediary layer of aerated earth under a flat, more or less impermeable riverbed to prevent worms from drowning - if remaining too long in some underground water table.

Oh, and there are rather solid, well swiming leaves too - lol.

By the way, do you think that the question of the missionaries is too offensive?

Answer 2

your answer ?

Comments

See above.   :-)

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your answer ? my friend

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Both my answer and the answer Marianne was hinting at, in her comments to my post directly above.

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Ok

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Hello, Suyanto, is the answer clear? It is only a fable, not real nature. And these puzzles or riddles are rather ancient.