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 her Birthday 2 days before Greg.

Tough Decisions

You are driving your car along the road in a very harsh snowy weather and reach a bus stop. On this bus stop you see that there are three people waiting – your best friend, a sick old lady and the girl of your dreams. The car unfortunately can accommodate only 2 people (including you), so you can not take all of them with you. What will be your choice?

The best solution is to let your friend drive the old lady and you stay with the girl of your dreams on the bus stop.

Potatoes and Wire

If you have two spheres, you can always make a loop with some wire, such that it fits both of them (for example you can shape it as a circle). If you have any two potatoes, can you do the same?

Yes, you can. Just take the two potato surfaces and intersect them. Their intersection will give you the shape of a wire which fits them both.

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Domino and Chess

Can you cover the chess board with 31 domino pieces, such that only two opposite corners are left uncovered?

The answer is NO. Every domino piece covers exactly one black and one white square on the chess board. Since initially you start with a different number of available white and black squares on the chess board, it is impossible to cover it with domino pieces.

Touching Pencils

Can you arrange 6 new identical pencils in space such that every two of them touch each other? What if you have 7 pencils?

Remark: The construction doesn’t need to be stable.

Below you can see solutions for 6 and 7 pencils. The construction with 6 pencils is stable, the construction with 7 pencils – not.