Last Problem:
At the chalkboard the teacher demonstrates the four factors of the number 6. That is to say, the whole numbers that can divide into 6 and leave no remainder. For the number six, the four factors are 1,2,3 and 6. (Remember, a number is always its own factor, as is 1.)
Between 1 and 100 there are five numbers that have exactly twelve factors. How quickly can you find all five?
Answer:
The five numbers between 1 and 100 that have twelve factors:
60: 1,2,3,4,5,6,10,12,15,20,30,60
72: 1,2,3,4,6,8,9,12,18,24,36,72
84: 1,2,3,4,6,7,12,14,21,28,42,84
90: 1,2,3,5,6,9,10,15,18,30,45,90
96: 1,2,3,4,6,8,12,16,24,32,48,96
Today’s Problem:
The sense of “Flatlanders” are limited to two dimensions (not three). If someone were to observe them from a point just “above” their world, the “Flatlanders” would have no way of seeing that particular observer.
What if you tossed a ball through the two-dimensional plane of Flatland? Would the Flatlander’s perceive the event as some sort of astronomical catastrophe? Describe exactly what the “Flatlanders” would see.