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.
A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?
There is an ancient kingdom where every married woman keeps information regarding the fidelity of other men. However, what they don't know is the fidelity of their own husbands. Also, there is an ancient belief that they don't tell each other about the fidelity of their husbands.
On a certain day, the queen of the kingdom declares that she has identified at least one unfaithful man in the kingdom. She allows the wives to identify and gives them authority to kill their husbands if they are unfaithful at midnight.
