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: $\displaystyle A,B,C,4,D,E,F,G,H,I,J,12$

You know that: $\displaystyle 4+C+D=333$

Solve to get: $\displaystyle C=329-D$

You also know that: $\displaystyle 4+D+E=333$

Solve to get: $\displaystyle E=329-D$

Therefore: $\displaystyle C=E$

Using the same method you get that: $\displaystyle B=D$

So you know that: $\displaystyle C+4+D=333$

Substitute: $\displaystyle C+4+B=333$

Solve: $\displaystyle 4=333-B-C$

Note that: $\displaystyle A+B+C=333$

Solve: $\displaystyle A=333-B-C$

Therefore: $\displaystyle A=4$

Using the same methods above you'll find that:

$\displaystyle A=4=F=I$

$\displaystyle B=D=G=J$

$\displaystyle C=E=H=12$

Remember that: $\displaystyle D=333-4-C$

Substitute: $\displaystyle D=333-4-12$

Then: $\displaystyle D=317$

So the pattern is: $\displaystyle 4,317,12,4,317,12,4,317,12,4,317,12$