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Find a relation between the following numbers:

First figure: center is 6, clockwise from top is 5, 1, 9. Second figure: center is 8, clockwise from top is 7, 4, 1. Third figure: center is 6, clockwise from top is 9, 7, 5. Fourth figure: center is 5, clockwise from top is a question mark, 1, 1.

We can use only elementary arithmetic (addition, subtraction, multiplication, and division). I found this puzzle in my old book. I think there is an arithmetic progression, because in the first shape (up left) we have 5+6+1=12, 1+6+9=16, 9+6+5=20. So we have sequence: 12,16,20. Common difference of successive members is d=4. For the second shape we have 13,16,19 so d=3. For the third shape 18,20,22, d=2. Finally for last shape we have d=1 but this is impossible. I think my answer is wrong because we delete center number in this puzzle and we must use center numbers in all shapes.

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    $\begingroup$ Which book was it? $\endgroup$
    – bobble
    Oct 18 at 14:01
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I'm not certain what the rules are for this, but using subtraction only you can have a progression where the result is figure 1 leaves you with 1, figure 2 with 2, figure 3 with 3, and figure 4 with 4:

1: 9-6 = 3; 5-3 = 2; 2-1 = 1
2: 8-4 = 4; 7-4 = 3; 3-1 = 2
3: 7-6 = 1; 9-1 = 8; 8-5 = 3

and lastly...

4: 5-1 = 4; 4-1 = 3; 7-3 = 4

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