Can you find a pattern and the missing number in the series given below?

100, 155, 258,? , 584, 819.

Solve the alphametic puzzle by replacing the alphabet with the number.

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There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?

If nine thousand, nine hundred nine dollars is written as $9,909,
how should twelve thousand, twelve hundred twelve dollars be written?

Spot 5 differences in two Christmas tree below:

This is a picture puzzle. You have to guess the name of the movie that can be related to the picture.

Without looking at a calendar, within a minute name, a boy's name using 5 consecutive 1st letters of 5 consecutive months

A Doctor always sneezes before the rain. Doctor sneezes, Will it rain?

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."?

In The 1st month of this year(the year 2013), I noticed that the date 13-1-13 (13 January 2013) is special.

This date is special as:

Date * Month = Year.

Can you figure out which year of this century has a maximum number of such dates?