But I assumed you wanted a brute force try and error shuffling.

> Do you mean like this (1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8)

Yes.

And there is only one possible solution

(1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1)

Trying 1e15 shuffles to finally get there seems like a good way to transform your hardware into an electric heater only.

there is only one possible solution

I count 7! = 5,040 solutions.

Trying 1e15 shuffles

There are 15!/8! = 32,432,400 permutations of the set (and for that matter 15! is only about 1.3e12). I don't see mention in Algorithm::Permute of how it handles duplicate elements, but I know that Algorithm::Loops handles them correctly.

That said I do agree with the thrust of your point. :)

I briefly looked at Algorithm::Loops by tye this morning but didn't quite understand it yet. Not quite intuitive I would say. BTW, my mathematical understanding is poor. Why is it 15!/8!?

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«The Crux of the Biscuit is the Apostrophe»

Darn!1!

> I count 7! = 5,040 solutions.

Of course you are right, what my my brain saw was that there is only one possible way to position the 1s.°

What I should better have shown is

(1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2)

which has only one solution

(1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1)

and 15! divided by 7! is still a very big number.

> I don't see mention in Algorithm::Permute of how it handles duplicate elements,

Assuming worst case means it's not handling duplicates differently. Many hear just use shuffle which certainly doesn't care.

Cheers Rolf
_{(addicted to the Perl Programming Language :)
see Wikisyntax for the Monastery}

°) off by one permutation group ;)

So this aren’t valid permutations?

karl@h3002993:~/src/perl$ ./pmute.pl
1 8 1 2 1 7 1 3 1 6 1 5 1 4 1
karl@h3002993:~/src/perl$ ./pmute.pl
1 3 1 4 1 7 1 5 1 2 1 6 1 8 1
karl@h3002993:~/src/perl$ ./pmute.pl
1 4 1 8 1 6 1 5 1 3 1 2 1 7 1
karl@h3002993:~/src/perl$ ./pmute.pl
1 5 1 8 1 2 1 4 1 6 1 3 1 7 1
karl@h3002993:~/src/perl$ ./pmute.pl
1 7 1 5 1 4 1 3 1 8 1 2 1 6 1
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FYI

karl@h3002993:~/src/perl$ time ./pmute.pl
1 4 1 3 1 2 1 6 1 5 1 7 1 8 1

real    0m0,081s
user    0m0,076s
sys     0m0,004s

karl@h3002993:~/src/perl$ lscpu
 Architecture:        x86_64
CPU op-mode(s):      32-bit, 64-bit
Address sizes:       46 bits physical, 48 bits virtual
Byte Order:          Little Endian
CPU(s):              1
On-line CPU(s) list: 0
Vendor ID:           GenuineIntel
Model name:          Intel(R) Xeon(R) CPU E5-2680 v3 @ 2.50GHz
…
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«The Crux of the Biscuit is the Apostrophe»

> So this aren’t valid permutations?

They are. Mea culpa.

You are listing the permutations of the fillers between the fixed 1s, hence 7! valid solutions.

See Re^8: Algorithm RFC: fast (pseudo-)random shuffle with no repetition for what I meant and try (1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2) instead.

If this doesn't convince you that try-and-error isn't a good idea, try adding even more 1s and 2s.

Cheers Rolf
_{(addicted to the Perl Programming Language :)
see Wikisyntax for the Monastery}

Somehow I also calculate differently:

CL-USER> (expt 10 15)
1000000000000000
CL-USER> (* 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15)
1307674368000
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«The Crux of the Biscuit is the Apostrophe»