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?

(I won't even TRY verse...sorry to disappoint you, but believe me you are better off...)

Taking into account that the glasses are negligibly thick, we can do this:

place the 4 unit glass inside the 16 unit glass, and push it all the way over to one side (say, the left). Then tip the 16 unit glass to the left until the right bottom edge of the 16 unit glass just reaches the water level. There will be 5 units left in the 16 unit glass.

Loose proof: the 4 unit glass has half the diameter of the 16 unit glass. If we left it out and tipped the 16, we would have 8 units. So the only thing is to show that the 4 unit glass displaces exactly 3 units. Since it has half the diameter, then the right edge of the 4 unit glass is directly over the center of the 16 unit glass. Thus when tipped, the water level is exactly half way up the 4 unit glass. Now if you think of the 4 unit glass as 2 2 unit glasses (one on top of the other) it is obvious: the lower one is completely submerged, and the upper one is half under the water, and half out of the water. Thus 3 units are displaced, so the total remaining is 5.

Posted by Brian Wainscott on 2003-08-11 16:02:47