As they were moving through the jungle, they met an old drunkard who insisted everyone should to swap their hats. The troop contains 64 people. In order to save time, each pair within the troop swaps hat with each other only once (i.e. no swapping is repeated). After a round of madness, Tintin notices that it is no longer possible to return all hats to their respective owners through more swappings. To sensibly resolve this maddening confusion, he decides to bring in even more hat-wearing guests in his troop, to allow for even more hat swappings. How many extra guests are needed to return all hats (including the extra ones) to their rightful owners? Note : Assume a person has exactly one mushroom.

China signed a currency swap deal with which country?

A boat is moving with a velocity 3 hat i+ 4hat j with respect to ground. The water in the river is moving with a velocity -3 hat i - 4 hat j with respect to ground. The relative velocity of the boat with respect to water is.

A boat is moving with a velocity 3 hat i+ 4hat j with respect to ground. The water in the river is moving with a velocity -3 hat i - 4 hat j with respect to ground. The relative velocity of the boat with respect to water is.

A boat is moving with a velocity 3 hat i+ 4hat j with respect to ground. The water in the river is moving with a velocity -3 hat i - 4 hat j with respect to ground. The relative velocity of the boat with respect to water is.

Sitting on the banks of the river, Aladdin and his friends see a group of sailors preparing their boat to sail south. Genie had never been to the south and this makes him interested in their sail and he wants to know where they were heading. Using his magical powers, he gathers everyone together and places a magical hat on some of the sailor’s head (i.e at least one person has a hat). The hat is magical as it can be seen by other people, but not by the wearer of the hat himself. The sailors find out about the hat and in order remove the hat, those ( and only those who have a hat) must dunk themselves underwater at exactly mid- night. If ai number of sailors dunk their hats on i-th day, find the sum of a_(i) x i for all the days till all the hats are removed. If there are 50 men and 7 hats find the sum.