3 Mislabeled Bins of Colored Balls
Atop a high shelf are three bins. You know that each of these bins
contains dozens of colored ping pong balls. These balls are all colored
either black or white, however, the shelf is too high for you to actually
see inside a bin. You can however, reach with your hand and pull a ball out of a bin and
see what color that individual ball is.
Each bin has a label on it. These labels read "Black Balls," "White Balls,"
and "Mixed Colors." You are told that indeed there is a bin which has only
black balls, one with only white, and one which is mixed, however, ALL of
the labels on the bins are incorrect.
By only drawing balls out of the bins, what is the minimum number of draws
you would need (and how would you do it) to determine the correct labeling
for the bins?
Measuring 4 Liters with only 3 and 5 Liter Jugs
You may have seen this one in Die Hard: With a Vengeance...
You are by a fountain of water with two jugs. One fills up to
exactly 3 Liters, while the other fills up to exactly 5 Liters.
A bomb next to the jugs has been activated and is primed to explode.
The bomb can only be defused by placing a jug, with EXACTLY 4 liters
of water in it, on a scale the bomb is connected to.
Note that these jugs are oddly shaped with no tick marks, so you
can't simply fill the 5 liter jug "four fifths" full to get 4 liters.
How can you fill the appropriate jug with EXACTLY 4 liters of
water so that you can deactivate the bomb?
2 Tablet A, 1 Tablet B, but Only Supposed to Take 1 of Each
Due to a sudden infection, your doctor has prescribed you to start taking
1 tablet of Axel Greez and 1 tablet of Betel Jewz every day.
You buy a bottle of each type of tablet, and go about your routine of
having one each day. Today however, as you are getting the tablets out of their
bottles, you accidentally shake 3 tablets out instead of 2.
Unfortunately, Axel Greez and Betel Jewz tablets look and smell exactly
the same. They are the same size, the same color, the same shape, in fact,
there is no way whatsoever to distinguish them now that they are out of the
bottle. Thus, you don't know which tablet is which in your hand. However,
by counting what's left in the bottles, you do know that, in your hand,
you have 2 Axel Greez tablets and 1 Betel Jewz tablet.
Note: Skipping a day of medication could be fatal. Eating
more than one Axel Greez tablet in one day could be fatal too.
What can you do to ensure no tablets go to waste, while also ensuring
you take your proper amount of medication?