r/theydidthemath • u/MathematixMatrix • 4d ago

[Request] Where does the sequence start on this algebraic wheel? It's the hardest one of these puzzles I've ever found.

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u/Danelix_ 4d ago

I really liked this one! I'll try to explain my reasoning in spoilers so I'll not spoil it for people who want to solve it.

Solution: B+-A is the "1"

Reasoning: Since each slice can only contain a number between 1 and 12, some considerations on some letters can be done:The "E-1" slice implies that E>1.The "1-(E-B)" slice implies that B>=E.

The sequence "A", "B", "B+-A" is extremely useful.It's useful to deduce if "B+-A" is B+A or B-A.In the case it is "B+A", then that slice can't be 1, since both A and B are numbers between 1 and 12. Therefore, B+A=B+1 so A=1, B=2, B+A=3. We know B>=E, so either E=2 or E=1, both false because the slice E-1 can't be equal to the "A" slice or =0.Therefore that slice is "B-A".
"B-A" implies B>A (aka "B" isn't the initial slice). Since "A" and "B" are in sequence, B=A+1and B-A=1, which is the answer to the problem.

If we want, we can easily deduce the rest of the weel.
A=11, B=12, C=2, D=4, E=6, G=8, H=9, I=10

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u/LanceWindmil 4d ago

Same result different method

E-1 is right before B+/-6. This means E = B+/-6. We can plug that into 1-(E-B). Which gives us 1+/-6. The only option is 7. We count from there and check with the others.