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If A, B, and C are three points on one line, D, E, and F are three points on another line, and AE meets BD at X, AF meets CD at Y, and BF meets CE at Z, then the three points ...

A rectangle which cannot be built up of squares all of different sizes is called an imperfect rectangle. A rectangle which can be built up of squares all of different sizes ...

A polyhedron dissection (or decomposition) is a dissection of one or more polyhedra into other shapes. Two polyhedra can be dissected into each other iff they have equal Dehn ...

A prime triplet is a prime constellation of the form (p, p+2, p+6), (p, p+4, p+6), etc. Hardy and Wright (1979, p. 5) conjecture, and it seems almost certain to be true, that ...

In a rectangular room (a cuboid) with dimensions 30^'×12^'×12^', a spider is located in the middle of one 12^'×12^' wall one foot away from the ceiling. A fly is in the ...

Hoggatt and Denman (1961) showed that any obtuse triangle can be divided into eight acute isosceles triangles. There are 1, 4, 23, 180, 1806, 20198, ... (OEIS A056814) ...

A twin prime cluster of order n is a collection of 2n consecutive prime numbers such that consecutive pairs form twin primes. Twin prime clusters were discussed by Mudge ...

A famous perceptual illusion in which the brain switches between seeing a young girl and an old woman (or "wife" and "mother in law"). An anonymous German postcard from 1888 ...

Any two rectilinear figures with equal area can be dissected into a finite number of pieces to form each other. This is the Wallace-Bolyai-Gerwien theorem. For minimal ...

Find a way to stack a square of cannonballs laid out on the ground into a square pyramid (i.e., find a square number which is also square pyramidal). This corresponds to ...