On Friday I posted this puzzle.  You have a straight-sided glass of orange juice that is filled to the brim like this…..

…and would like to share it with a friend.  You have no other drinking vessel, and nothing with which to measure the depth or content of the glass.  How do you make sure that you both get a fair share?

If you have not tried to solve it, have a go now.  For everyone else the answer is after the break.

You simply drink until the level of the liquid runs from the lip of the glass to the top of the opposite bottom rim, like this:

Then there will be exactly 50% left.  Did you solve it?  Any other answers?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

1. I did, yes. Supremely easy one this week. And no, I hadn’t seen this problem posed before.

2. Jimbo says:

As one gets older these questions become more a test of memory than of intelligence.

3. NO YOU DRINK UNTIL THE OTHER GUY SAYS “WAIT, THAT’S TOO MUCH!” THEN YOU FINISH IT. THEN YOU SAY “TOO BAD.”

1. treblekicked says:

This is correct

4. M says:

Got it. Was not hard.

5. Chrissie says:

The ACTUAL real life way this is done to prevent spilling any juice and thereby causing argument is…
Put finger on where you reckon half way down is then invite friend to drink whichever “half” they think is bigger to establish which of you drinks first. Drink down to finger.

1. Anonymous says:

Yeah, I went for the “pie rule” too. You draw a line on the glass, your friend decides if he wants the top or bottom half. Works for non-symmetric glasses too.

6. Fairly easy problem, I got it on my first guess. My second guess was “drink the entire glass, then pour another full glass for the other person”… followed by my third guess of “make paper cups out of spare printer paper”.

1. Jenny says:

Ooooh, I like the paper cups.

7. What about if you put in two straws and both suck at the same time?

1. Lindamp says:

Then the bigger sucker wins 😉

8. My answer was to place a vertical divider into the glass, that dissects the contents into two equal halves, and then drink with straws.

The downside is that unless it was watertight, as you drank one side the liquid from the other side would seep through, so it probably wouldn’t work.

Plus it requires the manufacture of said divider, by which time the other person has drunk the whole contents anyway…

Too easy!

10. ANuRa says:

I solved it although I never had seen the puzzle before. “Wow, I managed!” 🙂

11. Anonymous says:

Very easy.

12. Interesting (and in retrospect logical) solution.

I personally thought that as long as you trusted each other and had similar sucking capabilities, you take it in turns to have a sip until the juice has been drunk.

13. Lazy T says:

If the glass wasn’t symmetrical in section this solution would not work.

14. Karen says:

My solution was to carefully put it in the freezer, then cut it in half (preferably vertically, in case the pulp had settled to bottom).

15. Waldo says:

Yay for me — i got one!

16. Anonymous says:

Neither person drinks any. This is fair.

17. Anonymous says:

I drank it all- my half was on the bottom.

18. bill2350 says:

I drank it all- my half was on the bottom. Needless to say- I didn’t get this one right.

19. Cal says:

my answer was to pour it all away, then you both get exactly the same share

20. Tanya says:

I wouldn’t share a glass with anyone but that’s just me.

21. My answer was to freeze the orange juice, then cut it in half via eyeballing it, then each person has a popsicle which is better than orange juice ANYWAY.

22. Nick666 says:

meniscus? Makes it interesting

23. Anonymous says:

I let him drink if he enjoys it. He can drink more than a half, I don’t mind. Besides, I would find it tacktless if I stopped him exactly in 50%. What if earlier? Shame.

24. My answer was to take turns drinking gulps…one for me…one for you…etc. Not exact, but if you can agree ahead of time on what constitutes a gulp you can get pretty close.

25. Terry Stromberg says:

I was going to say each use the same size (1 each) large measuring spoons and take turns-tedious ,yes but more exact than the angled solution,but less elegant than others’ popsicle solution,theirs being the best.

26. Berber Anna says:

I couldn’t get over the idea of sharing a glass with someone else. Eww.

27. ChivNick says:

Drink the lot, refill the glass then give that to your friend. You both get the same amount.

28. michaelbeaton says:

I enjoy the fact that most people seem to have interpreted the “rule” of “fair share” as equal amounts… which is a normal reading of course… But not mandated by the proposition as writ.
So I particularly enjoy the solutions not so easy as some have said (based on the simple geometric solution) that address other aspects of the notion of Fair.