More Sisters on Average

Who have more sisters on average in a society: boys, girls, or is it equal?

Remark: Assume that each child is born a boy or a girl with equal probability, independent of its siblings.

The average number of sisters is roughly the same for both boys and girls. To see this, notice that every girl in every family contributes “one sister” to each of its siblings who are either a boy or a girl with equal probability. Therefore, every girl contributes on average the same number of sisters to the group of boys and to the group of girls. Since there is roughly the same number of boys and girls in the society, the average number of sisters for boys and girls is the same.

Send More Money

Replace every letter with a different digit between 0 and 9, such that you get a correct calculation.

The answer is 9567 + 1085 = 10652.

You can first see that M = 1. Then S = 8 or 9 and O = 0. MORE is at most 1098, and if S = 8, then E = 9, N is either 9 or 0, but this is impossible. Therefore S = 9, N = E + 1. You can check easily the 6 possibilities for (N, E) and then find the answer.

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Gerrymandering

The city has 49 districts that vote for blue, yellow, or purple as shown in the grid. Seven electoral regions are drawn up to elect a city council. Each region consists of seven districts and each region will elect one councilor. Can you gerrymander the map so that blue will win the majority?

The solution is shown below.

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.

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.

Man in the Elevator

One man who lives on the 12th floor every day takes the elevator to go to work. When he comes back in the evening, unless it is raining or there are other people in the elevator, he goes with it just to the 8th floor and then uses the stairs for the last 4 floors. Why does he do this?

The man is very short. Unless he has an umbrella or can ask other people to press the button for him, he can’t make the elevator go to the 12th floor.