A group of three smugglers is offered to smuggle a chest full of treasures across the dangerous river. The boat they possess is old and frail. It can carry three smugglers without the chest, or it can carry the chest and only two smugglers. The price for this job is extremely high, and the gang is more than interested in completing the job. Think of a strategy the smugglers should follow to successfully transit the chest and themselves to the other shore.
My mum once told me the following story: she was walking home late at night after sitting in the pub with her friends. She was then surrounded by a group of unfriendly looking people. They demanded: “money or your life?!” She was forced to give them her purse. She valued her life more, since she was pregnant with me at that time. According to her story she gave them two purses and two coins. Moreover, she claimed that one purse contained twice as many coins as the other purse. Immediately, I thought that the mum must have made a mistake or could not recall the details because of the shock and the amount of time that passed after that moment. But then I figured out how this could be possible. Can you?
Of the four inequalities \(2x > 70\), \(x < 100\), \(4x > 25\) and \(x > 5\), two are true and two are false. Find the value of \(x\) if it is known that it is an integer.
Winnie the Pooh has five friends, each of whom has pots of honey in their house: Tigger has \(1\) pot, Piglet has \(2\), Owl has \(3\), Eeyore has \(4\), and Rabbit has \(5\). Winnie the Pooh comes to visit each friend in turn, eats one pot of honey and takes the other pots with him. He came into the last house carrying \(10\) pots of honey. Whose house could Pooh have visited last?