Posts filed under ‘Sarah Flannery’
A beautiful learning puzzle from In Code: A Mathematical Journey
Suppose there are twenty people in a room.
If Alice and Bob are any two of them, and Alice knows Bob, then you may assume that Bob knows Alice. Furthermore, if Alice does not know Bob then, likewise, Bob does not know Alice.
Now, any individual among these twenty may know nobody else, or some but not all of the others, or know everybody in the room.
However, what might strike you as amazing on first thought is the fact that all twenty cannot each know a different number of people in the room. Put another way, there are at least two in the room who know exactly the same number of people.
Can you reason out why this must be?
One morning, exactly at sunrise, a Buddhist monk began to climb a tall mountain. The narrow path, no more than a foot or two wide, spiraled around the mountain to a glittering temple at the summit. The monk ascended the path at varying rates of speed, stopping many times along the way to rest and eat the dried fruit he carried with him. He reached the temple shortly before sunset. After several days of fasting and meditation he began his journey back along the same path, starting at sunrise and again walking at variable speeds with many pauses along the way. His average speed descending was, of course, greater than his average climbing speed. Prove that there is a spot along the path that the monk will occupy on both trips at precisely the same time of day.
Two trains are on the same track 100 km apart and each travelling at a speed of 50 km per hour are heading towards each other. A fly, initially on the front of one train, flies at 75 km per hour towards the oncoming train. On reaching it, the fly turns around instantaneously and flies back towards the other train. When it reaches the front of this train, it turns around again instantaneously and flies back towards the first train. How many kilometres will it have travelled before the two trains collide?
Study this paragraph and all things in it. What is vitally wrong with it? Actually nothing in it is wrong but you must admit it is most unusual. Don’t just zip through it quickly but study it scrupulously. With luck you will spot what is particular about it and all words in it. Can you say what it is? Tax your brains and try again. Don’t miss a word or symbol. It isn’t all that difficult.
An insurance salesman knocks on the door of a home in a housing development.
When a lady answers he asks, “How many children do you have?”
She replies, “Three.”
When he asks, “What are their ages?” she decides that he is too cheesy and refused to tell him.
After he apologizes for his apparent rudeness he asks for a hint about the children’s ages.
She says, “If you multiply their tree ages you get 36” (Their ages are exact numbers.)
He thinks for a while and then asks for another hint.
When she says, “The sum of their ages is the number on the next door,” he immediately jumps over the fence to determine this number.
This done, he returns to the lady and asks for one last hint.
“All right,” she says, “the eldest plays the piano!”
He then knows their ages. Do you?