What is next number in the pattern below:

131 517 192 123 ?

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.

There is a basket full of hats. Three are white and two are black. Three men, Tom, Tim, and Jim, each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves so Tom can see Tim and Jim’s hats, Tim can see Jim’s hat, and Jim can’t see anyone’s hat. Tom is asked what color his hat is and he says he doesn’t know. Tim is asked the same question, and he also doesn’t know. Finally, Jim is asked the question, and he does know. What colour is his hat?

Solve the counting riddle by identifying the number of triangles in the given picture.

You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?

Find the next number in the series.
1 10 24 43 67 ?

You were playing ping pong with your friend. Suddenly the ball fell into a narrow metal pipe that was imbedded in the concrete surface of the floor one foot deep. Now you don't have any other ball and you desperately want to take it out and play. You and your friend have your shoelaces, your tennis paddle and a plastic water bottle. However, the bottle cannot fit into the pipe.

How will you take the ball out?

A bus driver was heading down a street in Mexico. He went right past a stop sign without stopping, he turned left where there was a "no left turn" sign, and he went the wrong way on a one-way street. Then he went on the left side of the road past a cop car. Still - he didn't break any traffic laws. Why not?

Three doctors said that Bill was their brother. Bill says he has no brothers. How many brothers does Bill actually have?

Some friends went on a vacation to a resort. It was raining heavily and it kept raining for thirteen days.

When it rained in the morning, the afternoon was beautiful and when it rained in the afternoon, the day was blessed with a clear morning.

Overall, the friends experienced eleven nice mornings and twelve nice afternoons. Can you find out the number of days they spent on vacation?