Biden and Trump

Find a formula  

Suppose Biden and Trump stand for election to a golf club which has a hundred members. The one among them who gets more votes would be accepted as a new member. Sometime during the counting, the secretary of the club comes out and says that one person has got 49 votes and the other has got 36 votes as of that moment. The remaining votes are being counted. Someone says, since one has already got 49 votes, why don’t we stop the count and declare him the winner?  The Secretary says, "No. we have to be mathematically sure that one candidate has such a lead that he canot be defeated if the election continues".    

Let H be the votes earned by the leading candidate by that time.

Let L be the votes earned by the other  candidate by that time.

The total number of votes distributed, one per member = 100

Please note all members may not vote. Write the stopping condition in terms of H, L or both.  If the condition is satisfied, we should be able to stop the counting and declare the candidate with H votes the winner of the election.

Examples of conditions that are not good:   

                     H > L                  is not a correct stopping formula.

                     H + L < 100       is not a correct stopping formula.

Now comes a second problem. Assume that there are three candidates in an election. Only one candidate is to be elected. Can you find a stopping formula that says when the leading candidate is sure to win. 

Srinivasan Ramani   

6-Nov-2020  

Comments

Post a Comment

Popular posts from this blog

Flying all the way round the Equator!

Image
You know that drones are usually planes that fly without any pilots! They are controlled by a computer they carry.  Image Credit: NASA I think that very soon some drone will fly non-stop all around the equator, starting at some point on it and coming back to that point.  Suppose the drone flies at 100 miles per hour. How long will it take to fly a complete trip, flying over the equator?  You will have to know the distance involved. That depends on the size of the earth. Can you find out what is the distance the drone will have to fly? Then you can calculate how many hours it will take for the drone to fly this trip! Finally, you can convert the hours to days.  Talk to people who can help you with this calculation. Or perhaps, you can look up a book to find the distance involved. Ask the librarian in your school to show you an atlas. It will probably give you the answer. The librarian may help you find it.  Srinivasan Ramani 
Read more

The trick Julius Caesar used to play

Image
Julius Caesar adopted a tricky method of sending messages to his generals through messengers. What if his enemies caught hold of the messenger and read the message? They will then know Caesar’s plans. Caesar’s trick was to change the letters in the message. For instance, he could write “D” instead of “A”, “E” instead of “B” and so on. Every letter would be replaced by another three places further down in the alphabetical order. What do you do with “Y”? What is three places beyond “Y”? The trick is to think of the letters being arranged in a ring so that “A” follows “Z” and “B” follows “A”. In this ring you can go three places from “Y” and find “B”. The letter three places ahead of “Z” will be “C”. To encipher a message, that is to make it secret, we first choose a key. I recommend that you choose a whole number between 1 and 6 as the key. Suppose you choose 3 as the key. Now replace every letter in “TEXT” by one which is 3 steps away along the ring. Do you get “WHAW”? You can send ...
Read more