perplexus.info :: Just Math : Grape Consumption Conclusion

Grape Consumption Conclusion (Posted on 2016-03-08)

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.

See The Solution Submitted by K Sengupta

Rating: 3.3333 (3 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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