Sally lives in a place where six months of the year is mild summer and the temperature drops significantly the other six months. She owns a lake where there is a small island. She wants to build a house on the island and needs to get materials there. She doesn’t have a boat, plane, or anything to transport them to the island. How does Sally solve this problem?
Two natural numbers have a sum of less than 100 and are greater than one.
John knows the product of the numbers and Jacob knows the sum of numbers.
The following conversation takes place between them:
John: 'I am not aware of those numbers.'
Jacob: 'I knew you wouldn't be. I am not aware myself.'
John: 'Now I know them!'
Jacob: 'Now I know them, too!'
A thief enters a store and threatens the clerk, forcing her to open the safe. The clerk says, “The code for the safe is different every day, and if you hurt me you’ll never get the code.†But the thief manages to guess the code on his own. How did he do it?
There are 100 bulbs in a room. 100 strangers have been accumulated in the adjacent room. The first one goes and lights up every bulb. The second one goes and switches off all the even-numbered bulbs - second, fourth, sixth... and so on. The third one goes and reverses the current position of every third bulb (third, sixth, ninth? and so on.) i.e. if the bulb is lit, he switches it off and if the bulb is off, he switches it on. All the 100 strangers progress similarly.
After the last person has done what he wanted, which bulbs will be lit and which ones will be switched off?
