Prove that twice of ten is the same as twice of eleven.

I come in different shapes and sizes.
Parts of me are curved, other parts are straight.
You can put me anywhere you like,
but there is only one right place for me.
What am I?

Doctor Alex and a bus driver John are both in love with the same woman named Olivia. The bus driver need to go for a long trip of 10 days, Before he left he gave Olivia 10 apples.

Give it food and it will live; give it water and it will die.

A wooden log balances equally on the scales when weighed with three-quarters of a pound and three-quarters of a wooden log.

Can you calculate the weight of the entire wooden log?

What Does this text mean:

important=important

Count the number of balls in picture below:

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

What number comes next in this sequence:
7 8 5 5 3 4 4 _