12 positive integers are written in a row. The fourth number is 4, and the 12 number is 12. The sum of any three neighboring numbers is 333.Determine the twelve integers

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- Jan 28th 2007, 04:49 PMDragonPositive Integers
12 positive integers are written in a row. The fourth number is 4, and the 12 number is 12. The sum of any three neighboring numbers is 333.Determine the twelve integers

- Jan 28th 2007, 05:25 PMQuick
You have the numbers:

You know that:

Solve to get:

You also know that:

Solve to get:

Therefore:

Using the same method you get that:

So you know that:

Substitute:

Solve:

Note that:

Solve:

Therefore:

Using the same methods above you'll find that:

Remember that:

Substitute:

Then:

So the pattern is: