A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.
The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?
A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:
There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?
Count the number of triangles in the picture below:
The king of Octopuses has servants who have six, seven or eight legs. The distinguishing characteristics of the servants is that the one with seven legs always lie but the one with either six or eight legs speak the truth always.
One day, four servants meet and converse:
The black one says, 'We have 28 legs altogether.'
The green one says, 'We have 27 legs altogether.'
The yellow one says, 'We have 26 legs altogether.'
The red one says, 'We have 25 legs altogether.'
Can you identify the colour of the servant who is speaking the truth?
