Can you find a number that lies one third of the distance between 1/3 and 2/3?

Can you replace the X (both small and big x) with the numbers between 1 to 19 such that all the rows of 3 numbers between X (big x) sum to 23?

If a shopkeeper can only place the weights on one side of the common balance. For example, if he has weights 1 and 3 then he can measure 1, 3 and 4 only. Now the question is how many minimum weights and names of the weights you will need to measure all weights from 1 to 1000? This is a fairly simple problem and very easy to prove also.

Who always enjoys poor health?

Which of the following words don't belong in the group and why?
CORSET, COSTER, SECTOR, ESCORT, COURTS

Find The Missing Number In the Sequence.
6 25 64 ? 32 1

Solve The below Equation:

ALFA + BETA + GAMA = DELTA

In the Mexico City area, there are two Houses H1 and H2. Both H1 and H2 have two children each.
In House H1, The boy plays for Mexico Youth academy and the other child plays baseball.
In House H2, The boy Plays soccer for his school in Mexico and they recently have a newborn.

Can you prove that the probability of House-H1 having a girl child is more than that of House-H2?

It is an eleven letter word.
The first, second, third and fourth letters form a banquet's name.
The fifth, sixth and seventh letters form a car's name.
The eighth, ninth, tenth and eleventh letters form a mode of transport.

Can you identify what word it is?

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

O T T F F S S ?