## Saturday, August 15, 2009

### How drunk is your son?

Imagine you are visiting your son in college. In his dorm room you notice a completely full bottle of an unlabeled liquid smelling like alcohol. The next day, the bottle is partially empty with a temporary cork in it. You know who may have been drinking but would like to find out how much has been consumed exactly. How could you do it without leaving any clues? You happen to notice a ruler on your son's desk...

By the way, if your kids are far from the college age, replace "wine" with the "baby formula" in the above puzzle. How much did your baby sip?

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Need to test alertness level of your kid or friend remotely. See this creative solution.

rachel_t said...

Measure with the ruler the height of the liquid in a full bottle (h_full) and the current height (h_now). Bottles usually indicate on the label the amount in a new bottle (oz_indicated).

fraction consumed: (h_full - h_now)/(h_full)

multiply the fraction consumed by the ounces of a full bottle indicated on the label.

oz_indicated[(h_full - h_now)/(h_full)]

?

Maria said...

If would be right, except that our bottle is unlabelled and we have no indicator of the total amount of the liquid (wine or formula) inside.
Also, wine bottles have narrow top and are filled to the very top (at least this one). So, we can not assume that all the liquid initially was cylindrical. I will try to find a picture and post above.

The solution is worth finding. It is a brilliant trick and it is simple. Well, and of course the ruler comes handy. Take an old wine bottle, remove all the labeling, fill it to the top with water, then pour some amount out and you are half way to the solution :)

Alin Grin said...

Turn the bottle upside down and measure the height of the air cylinder which was created. Measure the diameter of the bottle’s bottom and apply the “volume of a cylinder" formula.
π*r^2*h= volume.

Maria said...

You got it!

I was at the playdate yesterday and shared this puzzle with both parents, using their wine bottle. One of them guessed the trick. But he did not enter it. Alin - you win, he - lost.

This is a great trick for the end-of-the-summer cocktail party.