# Le Monde puzzle 847 in Julia

**Wiekvoet**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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### Code

A function to check if a triplet has the desired property

In [1]:

function lemonde847(xx) a=[xx[1],2] b=[xx[2],8] c=[xx[3],4] sum(kron(c,kron(a,b))) end

Out[1]:

lemonde847 (generic function with 1 method)

Just a check – the function does indeed result in 1768 for the triplet 6 5 13.

In [2]:

lemonde847([6,5,13])

Out[2]:

1768

Check all combinations of numbers 1 to 60 excluding 2, 4 and 8. These need to be permuted later on. 60 may be a bit much, but how to calculate a bound? After all, imagine a set 1 3 60, that is only 1428. On the other hand, a combination with 59 and 60 should be too large. Hence we make a filter to exclude some. The rows where all three test numbers multiplied are higher than 1768. The remaining combinations are permuted and tested.

In [3]:

lemonde847([1,60,3])

Out[3]:

1428

In [4]:

totest = collect(combinations( symdiff(1:50, [2,4,8]),3))

Out[4]:

16215-element Array{Array{Int64,1},1}: [1,3,5] [1,3,6] [1,3,7] [1,3,9] [1,3,10] [1,3,11] [1,3,12] [1,3,13] [1,3,14] [1,3,15] [1,3,16] [1,3,17] [1,3,18] ⋮ [45,48,50] [45,49,50] [46,47,48] [46,47,49] [46,47,50] [46,48,49] [46,48,50] [46,49,50] [47,48,49] [47,48,50] [47,49,50] [48,49,50]

In [5]:

for i in 1:size(totest)[1] if prod(totest[i,])<1768 test2 = collect(permutations(totest[i,])) for j in 1:6 if lemonde847(test2[j,])==1768 print(test2[j,]') end end end end 6 5 13

Seems I found the answer; 6 5 13. The only thing left is to export the results. A bit of googling showed http://ipython.org/ipython-doc/stable/interactive/nbconvert.html.

### Final Notes

#### Conversion

In the end I converted the script via:

ipython nbconvert lemonde847.ipynb

The resulting file was opened in libreoffice and copied pasted into blogger. This gave a bit better results than conversion using

ipython nbconvert --template basic lemonde847.ipynb

and a copy paste of the .html directly in blogger.

Some post editing was done after examination of the preview of the post, but that is fairly normal for me.

#### Time usage

The calculation time was minimal. Most of the time was used in understanding Julia syntax, debugging, writing code, writing blog text, installation of pandoc. A lot of these things are one-off, but still, this last sentence took more time than the computation time.

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**Wiekvoet**.

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