Can you find out the remainder when 3^300 is divided by 5?

There are two beautiful yet remote islands in the South Pacific. The Islanders born on one island always tell the truth, and the Islanders from the other island always lie.
You are on one of the islands and meet three Islanders. You ask the first which island they are from in the most appropriate Polynesian tongue, and he indicates that the other two Islanders are from the same island. You ask the second Islander the same question, and he also indicates that the other two Islanders are from the same island.
Can you guess what the third Islander will answer to the same question?

Count the number of times the letter "F" appears in the following paragraph:

FAY FRIED FIFTY POUNDS OF
SALTED FISH AND THREE POUNDS
OF DRY FENNEL FOR DINNER FOR
FORTY MEMBERS OF HER FATHER'S FAMILY.

There is a family that live in a round house. The two parents go out for a movie and leave a babysitter to watch their son. They come back and the kid was not there. Some one kidnapped him. The maid said she was cleaning in a corner. The cook said he was making pizza. The babysitter said she was getting a board game. Who kidnapped him.

What begins with T, ends with T, and has T in it?

What is the value of 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1000?

How can you throw a ball as hard as you can and have it come back to you even if it doesn't hit anything there is nothing attached to it and no one else catches or throws it.

There were five men at church, and it started raining while they were outside. The four that ran still got wet, but the one that was still stayed completely dry. Why did he stay dry?

Can you find the odd number in the following?

2716, 4135, 5321 and 7145

What can you hold in your right hand, but never in your left hand?