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| Jack and Jill (Posted on 2003-08-11) |
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Jack and Jill went up a hill
And danced around with laughter,
Jack rolled down and lay on the ground,
And Jill came tumbling after.
"Hey, Jack," said Jill, "I'm feeling quite ill,
And my temperature's now getting hotter;
But I have these new caspules, so if it's not a hassle,
I need exactly five units of water."
Jack now was drained, and it would be such a pain,
To get water he'd have to go higher;
But he bent to her will, going back up the hill,
To get water, although he was tired.
On reaching the well, he suddenly fell,
And shattered his pail on the road,
But spying two lasses with cylindrical glasses,
He saw how to carry his load.
They're negligibly thick, he saw rather quick,
Praising himself for sagacity,
And what made it right was that both had same height,
Though obviously different capacity.
Sixteen and four were their volumes to pour,
And Jack filled the first up with water,
The second had none, but purely for fun,
He still took to Jill what he'd got her.
"Just tell me", whined Jill, as she looked for her pills,
"Why you brought me back sixteen and four?
Five from sixteen, is not easily seen."
But Jack said he'd something to show her.
How can sixteen units be reduced to five using these two glasses?
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Submitted by DJ
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Rating: 4.4091 (22 votes)
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Solution:
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(Hide)
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Tip the larger (16 unit) cylinder so that the water level goes exactly across the main diagonal.
Therefore, it is half full, and there are 8 units of water in it.
If the four-unit glass is held at that same angle, it will hold three-quarters of its total volume, or three units. Think of the 4-unit glass as two 2-unit glasses on top of each other, with the same diameter and half the height. In the diagram below, the bottom of these would be completely submerged, displacing two units of water, while the water level is across the main diagonal of the top one, meaning it displaces half its volume, or one unit of water. The entire four-unit glass, then, displaces a total of three units of water.
Therefore, since both glasses have the same height and negligible thickness, place the four-unit glass inside the sixteen-unit glass and tip them so that the water level is on the same diagonal, with the four-unit glass on the bottom.
The large glass will have eight units of water in it, but three of those are displaced by the smaller glass, leaving five units of water.
**
I modified and added to this puzzle-poem that appeared in The Daily Telegraph in October 1998, by Barry Clarke. |
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