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Comment by msvan | Hacker News Reader

The obligatory Python says that there are 120 solutions, or %0.03 of the possible permutations. It seems almost cruel to subject 8 year-olds to a problem like this, even if they have enough intuition to reduce the problem space a bit. Maybe it says more about the teacher than the students.

    from itertools import permutations
    
    def f(a, b, c, d, e, f, g, h, i):
        return a + 13 * b / c + d + 12 * e - f - 11 + g * h / i - 1
    
    solutions = [p for p in permutations(range(1, 10)) if f(*p) == 66]
    
    print(len(solutions))

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Agreed. I kept holding out hope that there was some clever solution I just couldn't see, but no, the only sane solution is to do exactly what you did and write a script. What's the point in making students slog through endlessly plugging numbers into a weirdly formatted equation?

Raise them to be diligent workers who never complain about boring tasks?

That script (with the -1 at the end replaced with the correct -10) does not work, at least on Python2. It misses the solution (1, 8, 3, 7, 4, 5, 2, 6, 9).

Here's a fixed script:

    from itertools import permutations

    def f(a, b, c, d, e, f, g, h, i):
        return a + (13 * b * i + g * h * c) / (i * c) + d + 12 * e - f - 11 - 10

    solutions = [p for p in permutations(range(1, 10)) if f(*p) == 66]

    print(len(solutions))

You need to swap the 1 at the end for an 11.

Also, this code for me returns 2672 solutions although I don't believe all are valid due to integer division. Perhaps a python 2 -> python 3 difference? (py2 here)

At the end should be 10.

And with checks to have only divisions without the remainder I get 20 solutions, the first one being (3, 2, 1, 5, 4, 7, 8, 9, 6)?

Yes, I get the same.

Edit - Ah yes, 10, sorry.

I have the same number, do you think there is a reason why they are not all valid? EDIT: actually the number I calculate is 2796. Also using Python 2..

Partly it might be due to needing "-10" at the end rather than -1 (I think I may have corrected it to -11 by mistake).

However, larger is the difference in how division works.

Python2: 3 / 2 => 1

Python3: 3 / 2 => 1.5

Would forcing the integer result fix this problem? Something like:

    def f(a, b, c, d, e, f, g, h, i):
        return a + int((13 * b * i + g * h * c) / (i * c)) + d + 12 * e - f - 11 - 10

If I try it like this, I still have the same number of solutions... Maybe I'm missing something..

EDIT: code formatting...

No, the problem is the other way around. Keeping them as integers and just using '/' is what's causnig the problem. You can either force them to be floats (not the result, the parameters in the calculation), or you can explicitly look for divisions that have remainders.

128 actually, you missed the last char of your snake. ( -1 should be -10 )

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