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.
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