Can you replace the question mark with the correct number?

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 ?

Can you convert the number zero(0) into a positive number using just one mathematical operator ?

Two prisoners Jack and Jill are locked in a cell.
There is open window approx 40 feet above the ground of the cell.
They are never able to reach there.

Then they plan to escape by a tunnel and they start digging out.
After digging for more than 20 days, Jill comes with the different plan and they escaped.

what was the plan ?

They are three errirs in this question. Can you find them?

A California farmer owns a beautiful pear tree. He supplies the fruit to a nearby grocery store. The store owner calls the farmer to see how much fruit is available for him to buy. The farmer knows the main trunk has 24 branches. Each branch has exactly 12 boughs and each bough has exactly 6 twigs. Since each twig bears one piece of fruit, how many plums will the farmer be able to deliver?

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

For an extra income, John decided to work at a Hotel for one hour daily. The manager offers him that they will pay him $11 after every 11 days.
However, John offered a different proposition to the manager. The offers stand as:
He will be paid just a penny on his first day.
Two pence will be paid on the second day,
Four pence will be paid on the third day.
And so on till the 11th day.

Should the Hotel manager accept his offer?

What has many keys but can’t open a single lock?

Prove that the below maths equation is true.

8 + 8 = 91