- #1

musicgold

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- Homework Statement
- I am trying to solve the puzzle shown below.

- Relevant Equations
- I could find the 3 equations shown below that appear to describe the situation.

First I tried to solve this with algebra, but there are not enough equations:

a+ b + c + d + e + f + g + h = 36

S = 12 + (d +f + a)/3 ........... ( d +f + a has to be a multiple of 3)

a + b + c = e + f

a + h + g = d + e

So I had to resort to the trial and error to find the solution below:

a, b, c, d :

a, h, g, f :

e :

Is there an elegant way / pattern to find other possible solutions?

Thanks

a+ b + c + d + e + f + g + h = 36

S = 12 + (d +f + a)/3 ........... ( d +f + a has to be a multiple of 3)

a + b + c = e + f

a + h + g = d + e

So I had to resort to the trial and error to find the solution below:

a, b, c, d :

**6, 1, 5, 7**a, h, g, f :

**6, 2, 3, 8**e :

**4**Is there an elegant way / pattern to find other possible solutions?

Thanks

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