What is more useful when it is broken?

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.

I am first found in caves, now prolific online; I am a depiction, a drawing, a symbol, or sign. I will convey whichever mood you could wish; or for that matter, a fist, flask, or fish. What am I?

Can you count the number of squares in the given picture?

If a zookeeper had 100 pairs of animals in her zoo, and two pairs of babies are born for each one of the original animals, then (sadly) 23 animals don’t survive, how many animals do you have left in total?

Can you find out the missing number in the grid?

Three fair coins are tossed in the air and they land with heads up. Can you calculate the chances that when they are tossed again, two coins will again land with heads up?

What does this rebus mean?

O
N
C
E
TIME

What country can make you shiver?

Can you make a fire with just a single stick?