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Ten people are sitting in a row, and each is thinking of a negative integer no smaller than -15. Each person subtracts, from his own number, the number of the person sitting to his right (the rightmost person does nothing). Because he has nothing else to do, the rightmost person observes that all the differences were positive. Let x be the greatest integer owned by one of the 10 people at the beginning. What is the minimum possible value of x?

mathbum  Sep 10, 2018
 #1
avatar+93866 
+1

Ten people are sitting in a row, and each is thinking of a negative integer no smaller than -15. Each person subtracts, from his own number, from the number of the person sitting to his right (the rightmost person does nothing). Because he has nothing else to do, the rightmost person observes that all the differences were positive. Let x be the greatest integer owned by one of the 10 people at the beginning. What is the minimum possible value of x?

 

I added a word because it was missing.

 

The means that the numbers must increase from left to right.

The left most cannot be smaller than -15 so the right most cannot be smaller than -6  

The minumum possible value of x is -6

Melody  Sep 11, 2018
 #2
avatar
+2

"Each person subtracts, from his own number, from the number of the person sitting to his right"

 

doesn't sound right to me, i think the original sentence is fine:

 

"Each person subtracts, from his own number, the number of the person sitting to his right"
 

i got the same answer (-6) but i think the numbers decrease from left to right (because every person subtracts the number of the person to his right from his own number, so the number of the person to his right must be strictly smaller)

 

 

 

i hope im right smiley

Guest Sep 11, 2018
 #3
avatar+93866 
+1

Yes you are right about the wording. 

The original wording is clumsy but I made it much worse and I expect my logic is no longer correct.

I will think about it more if i get around to it. :/

Melody  Sep 11, 2018

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