I change stature as I age, but my importance does not differ by age. My importance is manifested mostly when with my boss. When we part, I am of no importance.
A pencil. It gets shorter with use, but is no less important. Its impact is from the person using the pencil to write or draw. Without them, the pencil is just an idle tool.
In 2012 a class was divided into 2 groups. Their assignment was to find the names of at least 3 children who were born on the same day from 5 different months of 2011. These were the results:
Group 1 August 20: Oliver, William, and Adam. January 3: John, Alice, and Ken. September 7: Bruce, Shane, and Peter. June 11: April, Patrick, and Bobby. July 19: Trent, Julie, and Charles.
Group 2 March 1: Karl, Willie, and Patty. February 29: Blake, Kobe, and Wayne. December 24: Kyle, Chad, and Zoe. May 12: Matthew, Manny, and Adrian. November 20: Greg, Fiona, and Elizabeth.
The members of group 2 got an F on the assignment. Why?
Fred was almost done packing for the day, with five packages left. Unfortunately, Fred dropped the labels and had no idea which label went to which package. What is the probability that Fred managed to correctly label exactly four of the five packages?
Zero. If Fred had correctly labeled four packages, the fifth label would belong to the fifth package and all packages would be correctly labeled. Therefore it is impossible to mislabel exactly four packages.
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?