Intereting Posts

Uniqueness of prime ideals of $\mathbb F_p/(x^2)$
Minimal polynomial, determinants and invertibility
What is $\sqrt{i}$?
Finding the antiderivative of the product of two functions given only their derivative properties
Permutation isomorphic subgroups of $S_n$ are conjugate
Is my conjecture true? : Every primorial is a superior highly regular number, and every superior highly regular number is a primorial.
Lemma about the integral of a function with compact support
How to use Parseval' s( Plancherel' s) identity?
Show that if $ab \equiv ac$ mod $n$ and $d=(a,n)$, then $b \equiv c$ mod $\frac{n}{d}$
Complex cosine and sine
Give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain
Does a section that vanishes at every point vanish?
When do we have $\liminf_{n\to\infty}(a_n+b_n)=\liminf_{n\to\infty}(a_n)+\liminf_{n\to\infty}(b_n)$?
How to solve this Pell's equation $x^{2} – 991y^{2} = 1 $
Algorithm for multiplying numbers

$$M = \left(\begin{smallmatrix} a_1 & a_2 & a_3 & a_4\\ b_1 & b_2 & b_3 & b_4\\ a_1 & c_2 & b_2 & c_4\\ a_4 & d_2 & b_3 & c_4\\ b_1 & c_2 & a_2 & e_4\\ b_4 & d_2 & a_3 & e_4\end{smallmatrix}\right)$$ All of the equations equal to 26; augmented, the matrix would then have have “26” to the right of each row.

This is basically the “Star of David” that another user posted:

http://i.stack.imgur.com/mVHwZ.jpg

- What are some usual norms for matrices?
- List of connected Lie subgroups of $\mathrm{SL}(2,\mathbb{C})$.
- Solution of $A^\top M A=M$ for all $M$ positive-definite
- Looking for an identity for characteristic polynomial of a matrix to the power of n
- How to find a nonzero $2 \times 2$ matrix whose square is zero?
- Necessary and sufficient conditions for when spectral radius equals the largest singular value.

but I don’t think anyone has solved it like this.

- Why is this true: The only orthogonal projection that is also unitary from $\Bbb C^n$ to $\Bbb C^n$ is the identity
- CS231N Backpropagation gradient
- Writing an expression as a sum of squares
- $X$ is normal matrix and $AX=XB$ and $XA=BX$.why $A{X^*} = {X^*}B$ and ${X^*}A = B{X^*}$?
- Number of invertible 0-1 matrices
- Why are rotational matrices not commutative?
- Continued matrices-valued function
- Let $B$ be a nilpotent $n\times n$ matrix with complex entries let $A = B-I$ then find $\det(A)$
- Geometric series of matrices
- Basis of matrices with a variable

You have forgotten the very important condition that all integers between 1 and 12 must be used exactly once.

Though the equations themselves are linear and contain only 0 and 1 as coefficients, the constraint is very tough. I don’t think you could find an easy solution without integer programming, which is, like you may have known, NP-Hard and thus we have by now only exponential solutions, which are not better than brute force for such a small problem.

As I see, there are $960$ solutions ($80$ different solutions, ignoring rotation and mirror-transformation).

For example, $2$ of them:

Way of solving: “try-and-check”.

A).

Consider any values $a,h$.

For example, $a=5,h=6$.

Then possible values for $i,c$ are:

– $3,12$;

– $4,11$;

– $7,8$;

– $8,7$;

– $11,4$;

– $12,3$.

For these values you’ll get system of $5$ equations for $8$ variables. Reduction of system.

Sometimes such system will have no solutions.

B).

Consider $3$ any values for cells $a,c,e$.

Choose values for $b,d,f$, such that $a+c+e=b+d+f$.

When we’ll have values for $a,b,c,d,e,f$, we’ll get system of $6$ equations for $6$ variables ($g,h,i,j,k,l$).

But such system can have no solutions.

If you’ll use brute computer search, then there is not so much permutations of $12$ numbers: $12! = 479~001~600$ (a few seconds of computer work).

- The Sorgenfrey line is hereditarily Lindelöf
- Probability question.
- Relation of modulo multiplicative inverses: if $m = x^{-1} \pmod y$, is there $n$ such that $n = y^{-1} \pmod x$?
- general equation of a tangent line to a hyperbola
- Differential equation with a constant in it
- Let $\{X(t)\}$ be a Poisson process with arrival rate $\lambda>0$. Compute the conditional probability, $P(X(s) = x|X(t) = n)$.
- If G is finite group with even number of elements and has identity e, there is a in G such that a*a=e
- Prove that a covering map is a homeomorphism
- Does $ \int \frac{exp( -b(a+x)^{3/2})}{\sqrt{x}} dx$ have a solution?
- What's the connection between the indefinite integral and the definite integral?
- An alternative way to calculate $\log(x)$
- Quotient ring of Gaussian integers
- Probability vs Confidence
- Evaluate $\int_0^{\pi/4} \frac {\sin x} {x \cos^2 x} \mathrm d x$
- Solving recurrences with boundary conditions