O_er_t_o_

Complete the missing letters of the given word.

In a basket of apples,
when counted in twos, there was one extra
when counted in threes, there were two extra when counted in fours, there were three extra
when counted in fives, there were four extra
when counted in sixes, there was five extra.

However, if the apples were counted in sevens, no extra apple was left. Can you calculate the minimum number of apples that were present in the basket?

Samuel was out for a walk when it started to rain. He did not have an umbrella and he wasn't wearing a hat. His clothes were soaked, yet not a single hair on his head got wet. How could this happen?

Look at the below sequence of letters and tell us what the next letter should be:

O T T F F S S ?

As shown in the image, the nine Dogs are square fenced. By constructing just two square fences can you make sure that two Dogs cannot meet each other without crossing the fence?

What can you deduce from the following BrainBat?

CRY
LMKI

A thief enters a store and threatens the clerk, forcing her to open the safe. The clerk says, “The code for the safe is different every day, and if you hurt me you’ll never get the code.” But the thief manages to guess the code on his own. How did he do it?

Katniss and Peeta are liars. They both lie on some specific days.

Katniss lies on Fridays, Saturdays and Sundays. She speaks the truth on all other days.

Peeta lies on Tuesdays, Wednesdays and Thursdays. He speaks the truth on all other days.

Can you tell that one day of the week when both of them will say "Tomorrow, I will lie."?

A father told his three sons he would die soon and he needed to decide which one of them to give his property to. He said, “Go to the market and buy something large enough to fill my bedroom, but small enough to fit in your pocket. From this, I will decide which of you is the wisest and worthy enough to inherit my land.” They all went to the market, and each came back with a different item. The father told his sons to come into his bedroom one at a time and try to fill up his bedroom with their items. The first son came in and put some pieces of cloth he bought and laid them across the room, but it barely covered the floor. The second son came in and laid some hay on the floor, but there was only enough to cover half the floor. The third son came in and showed his father what he bought. He wound up getting the property. What did the third son show his father?

You see a mathematical expression in the picture. Can you think of a movie that this expression refers to?