# Positive Integers

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• Jan 28th 2007, 04:49 PM
Dragon
Positive 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 PM
Quick
Quote:

Originally Posted by Dragon
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

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\$