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Four numbers are written in a row.  The average of the first two numbers is 1.  The average of the middle two numbers is 2.  The average of the last two numbers is 3.  What is the average of the first and last numbers?

 May 6, 2020
 #1
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By "numbers" do you "integers", or did you mean "digits" ?

 May 6, 2020
 #2
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Four numbers are written in a row.  The average of the first two numbers is 1.  The average of the middle two numbers is 2.  The average of the last two numbers is 3.  What is the average of the first and last numbers? 

 

I don't have a formula, but just thinking about it, I see that

 

0, 2, 2, 4 will work.  So the average of 1st and 4th is 2.  

1, 1, 3, 3 will work too, the average of 1st and 4th is 2. 

 

There are other arrangements, as well, for example 2, 0, 4, 2 

 

I'm going out on a limb here and say that the average of the 1st and 4th numbers will always be 2. 

 

I haven't bothered to check out any negative numbers.  I'm tired of this problem. 

.

 May 6, 2020
 #3
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Let the four numbers be a, b, c & d respectively,

From information given: a+b = 2, b+c = 4 and c+d = 6

 

then (a+b) - (b+c) = a-c = 2-4 = -2

then (a-c) + (c+d) = a+d = -2+6 = 4

then (a+d)/2 = 4/2 = 2

then average of 1st and 4th numbers is 2

 May 7, 2020
edited by Guest  May 7, 2020

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