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Grape Consumption Conclusion (Posted on 2016-03-08) Difficulty: 3 of 5
A group of children held a grape-eating contest.
When the contest was over, the winner had eaten N grapes, where N is a positive integer.
The child in Mth place had eaten N + 2 – 2M grapes.
The total number of grapes eaten in the contest was 2016.

Find the smallest possible value of N.

No Solution Yet Submitted by K Sengupta    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
I could win this contest (spoiler) | Comment 1 of 4
Is Mth place supposed to be last place?  Are there any ties?

The puzzle did not specify, and the lowest N is reached by assuming that the answer to both of these is no.  
I did, however, assume that there is no tie for first place or Mth place.

Then N = 2 and M = 1.
1st place ate 2 grapes.
2014 other children ate 1 apiece.

Or do you think that M is supposed to be greater than 1?  Again, the puzzle did not specify that.  
If M must be > 1, then

Then N = 4 and M = 2.
1st place ate 4 grapes.
2nd place ate 2.
2010 other children ate 1 apiece.

Edited on March 8, 2016, 8:28 am
  Posted by Steve Herman on 2016-03-08 08:27:36

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