I ❤️ Math Day

During the winter term, students in 6th, 7th and 8th grades have been hard at work solidifying their understanding of Algebra.  On top of their daily work, we have also been tackling math puzzles as part of I ❤️ Math Day.  Below are two of the questions we have worked on so far.  If you scroll down to the bottom, you can see the answers provided by the students.  Several students will also be presenting their answers during Math Night on February 9th at 7PM.

Question 1:

A straight corridor has seven doors along one side.  Behind one of the doors sits a cat.  Your mission is to find the cat by opening the correct door.  Each day you can open only one door.  If the cat is there, you win.  If the cat is not there, the door closes, and you must wait until the next day before you can open a door again.  The cat is restless and every night it moves to sit behind another door.  The door it moves to is either the one immediately to the left or the one immediately to the right of where it was previously.

How many days do you need to make sure you will find the cat?

Question 2:

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 to 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.

For a more detailed answer, come to Math Night (February 9th at 7PM)

Question 1 Answer

It will take 10 days.  You open the 2nd door the first day, then the 3rd the second day, the 4th the third day, the 5th the fourth day, the 6th the fifth day.  Then 6th again the sixth day, 5th on the seventh day, 4th on eighth day, 3rd on ninth day and finally 2nd on the tenth day.  It should take no longer than 10 days.  No matter how the cat moves, it will be caught with this pattern within 10 days.

Question 2 Answer

Students presented the solution to this problem in many different ways.  Here is just one way of doing it.  These students assigned the various values that were not given in the problem and solved it using that data.  As you can see they  narrowed down the distance between the upward going monk and the downward going monk until they were in the same space at the same time.