A street of finite length has many houses on one side, which are numbered in consecutive order with 1, 2, 3, 4, ... Determine all house numbers where the sum of all house numbers before this house number is equal to the sum of all house numbers after it.

That's enough for this year.
I wish everyone a happy new year 2025.

Given 4 hummingbirds, each located at the vertex of a unit tetrahedron.
The birds begin to fly in such a way that all birds fly at the same speed and:
(1) Bird #1 always flies directly toward bird #2
(2) Bird #2 always flies directly toward bird #3
(3) Bird #3 always flies directly toward bird #4
(4) Bird #4 always flies directly toward bird #1
As one can imagine, the flying birds eventually meet and collide. (Assume the birds are very small.)

What is needed is the distance to the collision point of the hummingbirds.

As a Maple beginner, I am now interested in symbolic calculations in Maple. As before, I set a problem from a subject area that interests me in order to learn from professional answers.

Determine all regular square (n;n) matrices (determinant not equal to zero) that are commutable with every regular (n;n) matrix with respect to matrix multiplication.

(I know the solution from long ago.)

In the decimal system, we are looking for all natural numbers with at most six digits that only swap the order of the digits when multiplied by 2, 3, ..., 6.

In a plane, equilateral triangles D(i) with side lengths a(i)= 2*i−1, i = 1; 2; 3; ... are arranged along a straight line g in such a way that the "right" corner point of triangle D(k) coincides with the "left" corner point of triangle D(k+1) and that the third corner points all lie in the same half-plane generated by g. Determine the curve/function on which the third corner points lie!