You are decorating for spring and you’ve found a bargain. A huge box of beautifully decorated tiles, enough to provide a border in two rooms. You really can’t figure out how to arrange them. If you set a border of two tiles all around, there’s one left over. If you set three tiles all around or four or five or six there’s still one tile left over. Finally you try a block of seven tiles for each corner and you come out even. What is the smallest number of tiles you could have to get this result?
Laura saw that there were three pieces of candy left in a bowl on the kitchen table. She knew they were either chocolates or caramels but didn’t know how many there were of each. What is the probability that there is a piece of chocolate candy in the bowl?
I see much but change little, I am firm, irresolute, Powerful but gentle, I can rip apart mountains, Yet be moved by gentle stirrings, I am valued and wasted, I am life itself, And I give life to others.
A tree. A tall one can see long distances but don’t change much. They are strong and powerful, and the roots of a tree can slowly tear apart a mountain. The gentle stirrings of the wind can blow their branches and leaves. Trees are valuable as they provide wood and paper, but they are also wasted. And lastly, trees, like all plants, provide us with life-giving oxygen.
You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles and 2 empty bowls and instructs you to divide the 100 marbles into the two bowls. You can divide them however you want as long as all the marbles are in the bowls. You will be blindfolded and the bowls and marbles will be thoroughly mixed. You will then choose a single marble from one of the bowls. If the marble is white, you live. Black and you will be put to death.
How do you divide the marbles up so that you have the greatest probability of choosing a white marble?
Place one white marble in one bowl and place the rest of the marbles in the other bowl (49 whites, and 50 blacks).
This way you begin with a 50/50 chance of choosing the bowl with one white marble and living. Even if you choose the other bowl, you still have an almost 50% chance of picking one of the 49 white marbles. There are no guarantees in life, but this gives you the best change of surviving.
Zero. The Nile is the longest river in the world. Some claim the Amazon as the longest, but that too has no “S”es (that looks weird but I don’t know how else to write the plural of “s”). The Mississippi is the 4th largest river in the world according to a href=”https://en.wikipedia.org/wiki/List_of_rivers_by_length”>Wikipedia.
A merchant has 21 sacks of grain: 7 full, 7 half-full and 7 empty. He wants to divide them equally among his three sons. How can he do this, without transferring any grain between sacks, so each son has the same quantity of grain and number of sacks?