The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.
Find the five distinct digits N, R, I, C and H in the following
Let N be a six digit number with distinct digits. Find the number N given that the numbers N, 2N, 3N, 4N, 5N, 6N, when written underneath each other, form a latin square (that is each row and each. . . .
How many different solutions can you find to this problem?
Arrange 25 officers, each having one of five different ranks a, b, c, d and e, and belonging to one of five different regiments p, q, r, s. . . .
An equilateral triangle is constructed on BC. A line QD is drawn,
where Q is the midpoint of AC. Prove that AB // QD.
115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?
Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3!
Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational
symmetry. Do graphs of all cubics have rotational symmetry?