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.

Decode below rebus
D
N
A
T
S , D

Can you decipher the two rows to find the hidden word?

How do you go from 98 to 720 using just one letter?

As shown in the image, the nine Dogs are square fenced. By constructing just two square fences can you make sure that two Dogs cannot meet each other without crossing the fence?

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?

Find the next number in the series?
2, 12, 36, 80, 150, 252, 392, _ ?

The ages of a father and son add up to 66.
The father's age is the son's age reversed.
How old could they be?
(3 possible solutions).

In an Art Gallary, When the clock hit 11 am, Artist hung the painting number 30. When it struck 4 pm, he hung painting number 240 and when it struck 7:30 pm, he hung painting number 315.

Can you determine, which painting number will he hang when the time is 9:20 pm?

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?