SOLUTION: I was asked from some of my friends and I cannot solve this logical problem: Ex. We have 20 apples and we have to eat them for 5 days. Each day we must eat apples in an odd numb

Algebra ->  Finite-and-infinite-sets -> SOLUTION: I was asked from some of my friends and I cannot solve this logical problem: Ex. We have 20 apples and we have to eat them for 5 days. Each day we must eat apples in an odd numb      Log On


   

Question 176619: I was asked from some of my friends and I cannot solve this logical problem:
Ex. We have 20 apples and we have to eat them for 5 days. Each day we must eat apples in an odd number (ex. in 1st day 3apples in 2nd day 7 apples...) only in an odd number. Can anyone of you tell me how many apples we should eat from 1st to 5th day to complete the number of 20 apples! Thanks!
Found 2 solutions by solver91311, Mathtut:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The nth odd number is 2n+-+1 where n is a positive integer. So lets say you eat 2n%5B1%5D+-+1 apples the first day, 2n%5B2%5D+-+1 the second day, and so on. Then the sum of the apples eaten over a 5 day period would be:



Rearranging:

2%28n%5B1%5D+%2B+n%5B2%5D+%2B+n%5B3%5D+%2B+n%5B4%5D+%2B+n%5B5%5D%29+-+5+=+20

2%28n%5B1%5D+%2B+n%5B2%5D+%2B+n%5B3%5D+%2B+n%5B4%5D+%2B+n%5B5%5D%29+=+15

n%5B1%5D+%2B+n%5B2%5D+%2B+n%5B3%5D+%2B+n%5B4%5D+%2B+n%5B5%5D+=+15%2F2+=+7.5

Therefore at least one of the numbers n%5B1%5D through n%5B5%5D must not be an integer, violating the original assumption that the nth odd number is 2n+-+1 where n is an integer.

2%28n%5B1%5D+%2B+n%5B2%5D+%2B+n%5B3%5D+%2B+n%5B4%5D+%2B+n%5B5%5D%29 is an even number regardless of the values of n%5B1%5D through n%5B5%5D, presuming n%5Bi%5D is an integer and subtracting an odd number, namely 5 from an even number always results in an odd number. Therefore, eating an odd number of apples on each of an odd number of days results in an odd total.

Therefore, eating 20 apples total is impossible under the given conditions because 20 is an even number.

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
an odd number of the sum of odd numbers will always be odd
:
example 1+3+5=9
:
in general the sum%28+2n-1%2C+1%2C+infinity%29is always odd. where n is an integer
:
since we are talking about 5 days(odd) and each day we eat an odd number. The result will be an odd number of apples eaten. Therefore it is impossible to eat 20 apples under the stipulations given