Heads Up, Heads Down

You are blindfolded and on the table, in front of you, 50 coins are placed. You are told that X of them are heads up and the rest are heads down. Then you are asked to separate the coins into two groups and optionally flip some of them so that the number of heads in both groups becomes the same. How can you do this?

Separate the coins in one group of X coins and in another group of 50-X coins, then flip every coin in the first group. If in the first group there were Y heads up initially, then after flipping there will be X-Y – exactly the number of heads up in the second group.

Mixed Up Pills

One patient has two bottles with 30 pills each and every night has to take one pill from each of the bottles. Unfortunately one night after he takes out a pill from the first bottle and places it on the table, by accident drops two pills from the second bottle right next to it. The pills look identical, so he can not differentiate them. It is very important that he continues his treatment diligently throughout the entire timespan of 30 days. What should the patient do?

The patient should keep taking one pill from each bottle until there are 4 pills remaining – 1 in the first bottle and 3 on the table. On the 29th day he splits the pills in halves and takes one half from each pill. On the 30th day he takes the remaining halves of the pills.

Birthday Twins

Darma and Greg are twins, Greg being the older one by just few moments. However, several times in their lives, Darma celebrated her Birthday two days before Greg did. How is this possible?

Darma and Greg were being delivered on a plane/ship which was passing the 180th meridian. This way Greg got born on 1st of March and Darma got born on 28th of February. Therefore during leap years, Darma will celebrate here Birthday 2 days before Greg.