Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

One absent-minded ancient philosopher forgot to wind up his only clock in the house. He had no radio, TV, telephone, internet, or any other means for telling time. So he travelled on foot to his friend's place a few miles down the straight desert road. He stayed at his friend's house for the night and when he came back home, he knew how to set his clock. How did he know?

In the following series, a set of numbers is progressing with a particular pattern. Can you deduce that pattern and find the missing set?

(2 + 6), (21 + 6), (58 + 6), (119 + 6), ___

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

The person who makes it has no need for it. He who purchases it does not use it. The person who does use it does not know they are. What is it?

Place a mathematical symbol between the numerals 5 and 9 in such a way that the resulting number is greater than 5 but smaller than 9.

Which is the correct shadow of the bird?

In a boat, the father of a sailor's son is sitting with the son of the sailor. However, the sailor is not present on the boat.

Can this even be possible?

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

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?