Because the brain needs exercise too

A few tricky puzzles are a good way to keep the brain busy and the mood happy:

For the bad weather days, getting new idea to solve the world's problems, read some book on kindle make a good program but a good tricky puzzle is also satisfying.

Please feel free to suggest some more puzzles in thecomments :-)

Problem: Radioactive Balls.

There are 11 balls; two of them are radioactive. We have a tool in the form of a box. If we put several balls inside the tool, it can tell us whether or not there is a radioactive ball inside it. As this tool is very expensive to use, how can you find two radioactive balls using the tool the minimum number of times?

Problem: Coins

There are 12 coins. One of them is fake; it is either lighter or heavier than normal coins. Find the fake coin and say whether it is lighter or heavier by using the balance in the minimum number of steps.


This one is famous but there are some variations which I plan to give some thinking about:

1. Find a pre-determined solution which enabled mental calculation of the result; pre-determined in the sense that the 3 set-ups are in writing before any weighings, thus eliminating adjustments at weighings II and III. In addition, once the 3 set-ups are written and the 3 weighings are done, one can orally and immediately announce the number of the odd ball and whether it is light or heavy.

2. You have a balance scale and 13 coins, 1 of which are counterfeit.
4. You have a balance scale and 13 coins, 2 of which are counterfeit. The counterfeits weigh the same as each other, but are lighter than the rest. Can you determine the counterfeits in 4 weighings?
5. You have a balance scale and 16 coins, 2 of which are counterfeit. The counterfeits weigh the same as each other, but this time you don't know whether they're light or heavy. Can you determine the counterfeits (as well as their comparative weight) in 5 weighings?

Problem: Two Fuses

You have two fuses that both last one hour, and you have no other ways of telling time. The fuses may be thicker at some points, so in half an hour, the amount of fuse that has burned may or may not be half the length of the whole fuse. How do you measure 45 minutes worth of time?

 This one was known but what about this variation:


You have one fuse similar to the ones in the problem above. Is it possible to measure 20 minutes exactly?