Pascal's triangle/Puzzle: Difference between revisions
Content added Content deleted
No edit summary |
|||
Line 314: | Line 314: | ||
|5 11 13 4 8| |
|5 11 13 4 8| |
||
+-----------+</pre> |
+-----------+</pre> |
||
=={{header|Mathematica}}== |
|||
We assign a variable to each block starting on top with a, then on the second row b,c et cetera. k,m, and o are replaced by X, Y, and Z. We can write the following equations: |
|||
<lang Mathematica> |
|||
b+c==a |
|||
d+e==b |
|||
e+f==c |
|||
g+h==d |
|||
h+i==e |
|||
i+j==f |
|||
l+X==g |
|||
l+Y==h |
|||
n+Y==i |
|||
n+Z==j |
|||
X+Z==Y |
|||
</lang> |
|||
And we have the knowns |
|||
<lang Mathematica> |
|||
a->151 |
|||
d->40 |
|||
l->11 |
|||
n->4 |
|||
</lang> |
|||
Giving us 10 equations with 10 unknowns; i.e. solvable. So we can do so by: |
|||
<lang Mathematica> |
|||
eqs={a==b+c,d+e==b,e+f==c,g+h==d,h+i==e,i+j==f,l+X==g,l+Y==h,n+Y==i,n+Z==j,Y==X+Z}; |
|||
knowns={a->151,d->40,l->11,n->4}; |
|||
Solve[eqs/.knowns,{b,c,e,f,g,h,i,j,X,Y,Z}] |
|||
</lang> |
|||
gives back: |
|||
<lang Mathematica> |
|||
{{b -> 81, c -> 70, e -> 41, f -> 29, g -> 16, h -> 24, i -> 17, j -> 12, X -> 5, Y -> 13, Z -> 8}} |
|||
</lang> |
|||
In pyramid form that would be: |
|||
<lang Mathematica> |
|||
151 |
|||
81 70 |
|||
40 41 29 |
|||
16 24 17 12 |
|||
5 11 13 4 8 |
|||
</lang> |
|||
=={{header|Oz}}== |
=={{header|Oz}}== |