A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of the renovation of the kingdom to meet future security needs, he asked his chief architect to lay down a new play in a manner that all of his 10 castles are connected through five straight walls and each wall must connect four castles together. He also asked the architect that at least one of his castles should be protected with walls. The architect could not come up with any solution that served all of King's choices, but he suggested the best plan that you can see in the picture below. Can you find a better solution to serve the king's demand?
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?
How many triangles are there in the picture below?
