Project Euler Forum

Let AE, BF and CG be the angle bisectors of triangle ABC. Let the points E, F and G lie on BC, AC and AB, respectively. Let M denote the incenter of ABC. Prove that if the sum of the areas of the inside triangles MCF, MAG and MBG equals half the area of triangle ABC, then ABC is isosceles. In otrher...

Thank you, smart approach - understood. But rather than working with a transition matrix (I´m grade 9 and haven´t heard of such thing) I would try to formulate a recursive formulation taking me step wise from layer to layer thereby differentiating between the possible protrusions of 0, 2 or 4 cuboid...

Appreciate your advice, thank you. Thus, I start in the first 2 x 2 layer of the 2 x 2 x 12 container. Some of the 2 x 1 x 1 elements will cross the first layer and protrude into the second layer. With 4 squares in the layer there are 4^2 = 16 possibilities for protrusions to the next layer. Conside...

In how many different ways can 24 identical boxes (cuboids), each measuring 1 x 1 x 2 be packed into a single (cuboid) container measuring 2 x 2 x 12? This is a math problem from school to which I do not have a clue. I tried to define possible sub-arrangements of two 1 x 1 x 2 cuboids and tried find...