Tag: math & puzzles

Long ago, there was a king who had six sons. The king possessed a huge amount of gold, which he hid carefully in a building consisting of a number of rooms. In each room there were a number of chests; this number of chests was equal to the number of rooms in the building. Each chest contained a number of golden coins that equaled the number of chests per room. When the king died, one chest was given to the royal barber. The remainder of the coins had to be divided fairly between his six sons. The Question: Is a fair division possible in all situations?

Two whole numbers, m and n, have been chosen. Both are unequal to 1 and the sum of them is less than 100. The product, m × n, is given to mathematician X. The sum, m + n, is given to mathematician Y. Then both mathematicians have the following conversation: X: "I have no idea what your sum is, Y." Y: "That's no news to me, X. I already knew you didn't know that." X: "Ahah! Now I know what your sum must be, Y!" Y: "And now I also know what your product is, X!" The Question: What are the smallest values of m and n?

You are a participant in a quiz. The quizmaster shows you three closed doors. He tells you that behind one of these doors there is a prize, and behind the other two doors there's nothing. You select one of the doors, but before you open it the quizmaster deliberately picks out a remaining empty door and shows that there is nothing behind it. The quizmaster offers you a chance to switch doors with the remaining closed door. The Question: Should you stick to your choice?

Someone shows you two boxes and he tells you that one of these boxes contains two times as much as the other one, but he does not tell you which one this is. He lets you choose one of these boxes, and opens it. It turns out to be filled with \$10. Now he gives you the opportunity to choose the other box instead of the current one (and skip the \$10 of the first box), because the second box could contain twice as much (i.e. \$20). The Question: Should you choose the second box, or should you stick to your first choice to maximize the expected amount of money? A Hint : If you have \$10, and you could double this with a chance of 1/2, or half it with a chance of 1/2, one would expect an average of 1/2 * \$20 + 1/2 * \$5 = \$12.5 (so you would expect to gain $2.5)!...

In a city called Veldhoven the following facts are true: No two inhabitants have exactly the same number of hairs. No inhabitant has exactly 40360 hairs. There are more inhabitants than there are hairs on the head of any one inhabitant. What is the largest possible number of inhabitants of Veldhoven (knowing that the number of inhabitants is not infinite)?