A six-digit number represented by ABCDEF (each letter represents a different number) can be multiplied by 2, 3, 4, 5, and 6 and yet no new digits appear in the result. As a matter of fact, all the digits are rotated. What is the number?
5 minutes. It takes each machine 5 minutes to make a shirt, so if you have all 100 machines running at the same time, they’ll produce the 100 shirts in 5 minutes.
They are the origins of the names of each day of the week.
Sunday – Sun day. Monday – Moon day. Tuesday – Tiw’s or Týr’s day, the god of single combat, son of Odin. Wednesday – Woden’s or Odin’s day, god of poetry and of the dead. Thursday – Thor’s day, god of thunder, son of Odin. Friday – Frigg’s day, goddess of the clouds, wife of Odin. Saturday – Saturn’s day, god of fertility and agriculture.
I give you a group of three. One is sitting down, and will never get up. The second eats as much as is given to him, yet is always hungry. The third goes away and never returns.
There is an abandoned aquarium in an empty house. The aquarium has three large fish and three small fish. But after a week, one large fish and two small fish die.
Three philosophers are taking a nap under a tree. While they’re asleep, a small boy smears their noses with red berries. When they awake, they each begin to laugh, thinking the other two are laughing at each other.
But then one philosopher stops laughing, realizing his nose is red too. How did he come to this conclusion?
Let’s call the philosopher’s A, B and C. A reasoned that B was confident his nose wasn’t red. If B saw A’s nose wasn’t red, he would be surprised that C was laughing, because C would have nothing to laugh at. But B wasn’t surprised, therefore, A correctly reasoned his nose was smeared.
Imagine an HIV test that is 95% accurate (false positive rate of 5%) and around 2% of the tested population is infected with HIV. What is the probability that you actually have HIV when your test comes back positive?
She will always need to give you 5 apples. You both need at least 5 apples to begin with, but apart from that it doesn’t matter exactly how many you each have. When she gives you 5 you will have 10 more than her because she will lose 5 and you will gain 5, resulting in a net difference of 10.
For example, if you each have 25 apples and she gives you 5 of hers, she will be left with 20 and you will now have 30, precisely 10 more than she has.