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?

Guest May 6, 2020

#2**0 **

*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 1^{st} and 4^{th} is 2.

1, 1, 3, 3 will work too, the average of 1^{st} and 4^{th} 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 1^{st} and 4^{th} numbers will always be 2.

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

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Guest May 6, 2020