# Positive Integers

• Jan 28th 2007, 05:49 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, 06:25 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: $A,B,C,4,D,E,F,G,H,I,J,12$

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

Solve to get: $C=329-D$

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

Solve to get: $E=329-D$

Therefore: $C=E$

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

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

Substitute: $C+4+B=333$

Solve: $4=333-B-C$

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

Solve: $A=333-B-C$

Therefore: $A=4$

Using the same methods above you'll find that:

$A=4=F=I$

$B=D=G=J$

$C=E=H=12$

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

Substitute: $D=333-4-12$

Then: $D=317$

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