Again, please private message me the answer!

Let n be an integer greater than 0. The numbers 1,2,3....,n are written on a blackboard. We decide to erase from the blackboard any two numbers, and replace them with their nonnegative difference. After this is done several times, a single number remains on the blackboard. For which values of N can this number equal 0?


Hint #1: Try small cases.

Hint #2: To rule out a value of n, consider parity. (This means look at whether the number is even or odd.) As a function of n, can you say something about the parity of the last number that remains?

Hint #3: To show that it's possible for a value of n, you may want to try to build on smaller values of n. What proof technique does this suggest?

lololololololololll  Jun 28, 2018

I oppose questioners having answerers "private message" them the answers. This is because of three reasons:




How are we supposed to know whether or not someone has already answered the question, or are you just expecting 20 people to "private message" you the answer. It's a waste of time for all the effort in composing the answer to satisfy your uncanny request. 




"Private messaging" you do answer prevents other users from viewing the solution. This way, other people cannot learn, just to satisfy your uncanny request.




To my knowledge, you do not receive points from sending private messages. Not only you are preventing others from learning, and causing confusion for the answerers, you are completely screwing up the point system. 

GYanggg  Jun 28, 2018

Hi Gavin  and others,


When people make a post like this I think it is intended as a game.

The asker is implying that he/she knows the answer and is asking you to accept the private challenge to answer it.

I personally would be unlikely to answer a question like this at all, I do not think it is intended for the mathematicians that frequent this site regularly.

Then again, with a heading like 'help' I am quite likely wrong, and I would advise people to simply not answer at all.


No, the answerer cannot get points for a private answer.


I do take your point that it stops others learning from the answer but if lol is a nice person I would expect him/her to be prepared to provide the answer privately.


Perhaps lol is hoping to attract like minded people to answer him privately so that he/she can go on and form a private freindship with one or more of them? 

Melody  Jul 2, 2018
edited by Melody  Jul 2, 2018

Here's a hint: try using induction


(Use induction to prove that if it is possible to erase the numbers 1, 2, 3, ... , n and remain with 0 then it is also possible to erase the numbers 1, 2, ..., n, n+1, n+2, n+3, n+4 and remain with 0)

Guest Jun 28, 2018

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