An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?
While handling a project, the landscaper is asked by the owner of the mansion that he wants four trees in front of his mansion that are exactly equidistant from each other.
Two boys were admitted to a school. When the headmaster asks them about their parents, they tell him that they have same parents (father and mother). On further inquiry, it turns out that they both share the same date for their birthday.
"Are you twins," ask the headmaster.
"No," replies the boys.
A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 3 hours to fill the tank with the large inlet pipe. On the other hand, it takes 6 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 9 hours.
What fraction of the tank (initially empty) will be filled in 0.64 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).
Using the clues below, what four numbers am I thinking of?
The sum of all the numbers is 31.
One number is odd.
The highest number minus the lowest number is 7.
If you subtract the middle two numbers, it equals two.
There are no duplicate numbers.
In 2011, people playing Foldit, an online puzzle game about protein folding, resolved the structure of an enzyme that causes an Aids-like disease in monkeys. Researchers had been working on the problem for 13 years. The gamers solved it in three weeks.
