Solution for 4/3/10 puzzler is all wet

Did anyone else find the solution for the 4/3 puzzler to be all wet? (Using a 4-oz glass and a 9-oz glass, measure 6 ounces of water in fewest steps.) Eight steps indeed. Try four steps:

1. Fill the 4-oz glass.

2. Empty the 4-oz glass into the 9-oz glass.

3. Tip the 4-oz glass 45 degrees and fill the glass so that the bottom of the glass is just covered and the water just touches the bottom inside rim of the glass. The glass is exactly half full at this point.

4. Empty the 4-oz glass into the 9-oz glass.

QED. Six ounces of water in four steps.

Anyone have a better solution?


How do you know the glass is at exactly 45 degrees? No compass or ruler supplied.

So step 3 is bogus to me.

This also assumes the 4 ounce glass is a perfect cylinder. Not likely.

When I first saw your solution, I felt kind of dumb. Then, like texases, I worried about the shape of the glass, but I have neither gotten out the calculus book nor conducted real world experiments to verify that that is a concern. We can dismiss sircuitsmith’s critique out of hand: gravity is supplied. No compass(?!) or ruler(?!) necessary. No carpenter’s level supplied either (That would be the right tool for the job. (That’s how you do it, son (thanks Charlie Daniels)).

As stated, this only works if the glass is perfectly cylindrical. No 45 degree tilt needed, just fill the glass so that the bottom is -just- covered and the water -just- reaches the rim.

Good practical solution, though, given the cylindrical constraint.

I now realize the tilt would be 45 degrees only if the diameter and height of the glass were equal.

p.s. to Zombie: while Charlie Daniels isn’t a friend of mine, you’re no Charlie Daniels.


"I now realize the tilt would be 45 degrees only if the diameter and height of the glass were equal.

p.s. to Zombie: while Charlie Daniels isn’t a friend of mine, you’re no Charlie Daniels."

You got that right, son.

My thought, fill the 9 oz glass, dump 4 oz into 4 oz cup then dump, dump 4 oz into cup then dump, dump last oz from 9 oz glass into 4oz cup then mark the level. Dump that oz into 9 oz cup, fill to mark dump that into 9 oz cup, fill 4oz cup dump into 9 oz cup and walaa, 6 oz. 7 steps.

No marking, I would think…

You need the mark for the second oz! Funny story I scored highest on an IQ test in the history of the company for an IT job at an insurance company, and did not get the job, no I am not a whacko, but I always did wonder about that loss of opportunity.

I solved the puzzle exactly the same way. I answered this same puzzle over 30 years ago while attending college. I got the answer right then but I guess they want a longer answer now. You don’t need a ruler or compass when tilting 45 degrees because the water will touch the lower edge of the glass lip and the upper edge of the bottom.

Will that work with a glass shaped like the classic Coca-Cola glass? Or any glass that isn’t a perfect cylinder (note that the shape of the glass wasn’t specified in the Puzzler) such as a truncated cone or truncated pyramid glass?

No in both cases.

The reason we can say it’s half in the case of a cylinder is because the volume of water is equal to the volume of air (within the volume taken by a full glass). As somebody noted previously, it’s not a 45 degree angle that’s important, it’s that the bottom is just completely covered and the lip is not covered at all.

In the case of a truncated cone, consider the extreme example of the cone tip getting smaller and smaller, so that in effect, it’s not even truncated (or even truncated just a tiny bit). When it’s tipped on its side, the area filled with water obviously has less water than the area filled with air.

Similarly in a classic Coca-Cola glass, when it is tipped, the larger end is holding more air than water.

Such was my intuition. That’s why tipping the glass is not a solution for this Puzzler, because the shape of the glass was not specified.

Agree that estimating half a glass works only if glass is cylinder.

OTOH, in the spirit of the original description - listen for it -
Step 1: fill 9 oz,
Step 2: pour 4 oz into other glass and discard.
Step 3: dump remainder (5oz) into your SHOE.
Step 4: refil 9oz
Steps 5 and 6: discard 4oz measures using small glass twice
Step 7: pour remaining 1 oz into SHOE = 6 oz!

Assumes a container (SHOE) not in the original puzzler.

How about a mouth?

Depending on how you define “cylindrical” it may not require a cylindrical glass.

Tilting the glass so that when the water is just touching the lip on one side and the opposite edge of the glass’s bottom the empty volume equals tghe wet volume does require certain symmetries. For example, an avant garde glass with an octagonal (horizontal) cross section would work, but a glass wih a pentagonal cross secion wouldn’t. The vertical cross section must be top-botom symmetrical, as well. For example the stupid plastic cups they “give” you the $5 coke in on an airplane wouldn’t work; a "fotball glass would. (“Football” glass: Blow a football shaped object, cut the ends at equal diameters, seal one end which becomes “the bgotom”.)

BTW: Step 3 is really two steps, “tilt” and “fill”.

Zappa would NOT dig you, Zombie.

Dan, I tried your tilt idea using a water glass. In theory it works, but practically not very accurate as the water sloshes around and has a lot of surface tension. Step 3 is really two or more steps due to the trial and error. So I stand by the official solution of 8 steps.