Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.

For this puzzle, you might have to find logic in something illogical. But hey, it's fun and a healthy little break from your strenuous puzzle-solving sessions.

Can you decipher the meaning in the following cluster of letters?

ITIT,NCENTCENT

An octopus has 8 legs. A hippogriff has 6 legs and 2 pairs of wings. A sphinx has 6 legs and one pair of wings. Now we have all 3 kinds and a total of 18 insects in a cage. We have a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

If 2 workers can complete painting 2 walls in exactly 2 hours.

How many workers would be needed to paint 18 walls in 6 hours?

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.

Assume there are approximately 5,000,000,000 (5 billion) people on Earth. What would you estimate to be the result, if you multiply together the number of fingers on every person's left hand? (For the purposes of this exercise, thumbs count as fingers, for five fingers per hand.) If you cannot estimate the number then try to guess how long the number would be.

Lifeless eyes on my smiling face and watch your child's sleeping place. In their dreams they hold me tight. What am I?

A worker is to perform work for you for seven straight days. In return for his work, you will pay him 1/7th of a bar of gold per day. The worker requires a daily payment of 1/7th of the bar of gold. What and where are the fewest number of cuts to the bar of gold that will allow you to pay him 1/7th each day?

I am taken from a mine and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?

1. Where does Easter come from before Valentine's Day?

2. Do you know what is in the middle of Valentine's?

3. What did the lady bee say to the man bee on the occasion of Valentine's Day