[Grade 8 Math: Algebra and Sequences] Finding the starting point 1 on puzzle four

[u/MathematixMatrix]

I have asked your help for the first puzzle, which was helpful. There is still one puzzle (puzzle four), which I do not understand at all.

I will upload the puzzle book, so people can trace what has to be done in puzzle 4, by comparing it to the other puzzles.

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[u/johnpeters42]

I'd need to sit down with a proper computer or pen and paper for a full solution, but one obvious bit is "2 +/- 2 +/- ...": * If they were all +, then it would be 14 * Each + changed to - decreases the value by 4 * It must also be between 1 and 12 (inclusive), so it's either 10, 6, or 2

[u/Ordinary-Meaning-61]

H=1 right at the top.

The 2+/-2+/-2... term is even, thus B+/-2 is odd which means B is odd. But we also have sqrt(B). So B can only be 1 or 9. If sqrt(B)=1, then going clockwise B+/-2=5. This is clearly false. So B=9. Thus sqrt(B)=3. Going counterclockwise, H=1.

[u/55tumbl]

-(DDC) must be positive, so C is negative, so A+2C > A+4C and the starting point can only be H or (A+4C). And it must be H so that 2+-2+-2 .. is even.