A graph is a collection of vertices and edges. Vertices are the dots and edges are the lines that connect the dots. On the left, all edges can be redrawn (curved lines are allowed and moving vertices is allowed) such that no edges cross each other and each vertex is still connected to the same other vertices. These graphs are called planar.

Adjacent-numbered pages:
BP900 BP901 BP902 BP903 BP904  *  BP906 BP907 BP908 BP909 BP910

nice, precise, allsorted, notso, math, left-null, preciseworld

connected_graph [smaller | same | bigger]

Molly C Klenzak

The rows in the panels on the right hand side show all the ways you can divide a certain number of dots between a certain number of bins, ignoring which bins they are placed in.

Adjacent-numbered pages:
BP899 BP900 BP901 BP902 BP903  *  BP905 BP906 BP907 BP908 BP909

solved, left-null, grid, left-listable, right-listable

Molly C Klenzak

Which two sides are the long sides and which side is the short side, or equivalently which angles are the wider angles and which angle is the narrower angle, is the only relevant information to consider for each triangle. Triangles are all assumed isosceles and congruent to one another.

All examples in this Problem feature four of these triangles connected by corners and/or edges.

BP897 was conceived as a false solution for this.

Adjacent-numbered pages:
BP893 BP894 BP895 BP896 BP897  *  BP899 BP900 BP901 BP902 BP903

hard, precise, allsorted, notso, math, preciseworld

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Molly C Klenzak

Another solution is that right examples can be folded down flat onto one isosceles triangle while left examples cannot.

All examples in this Problem feature four isosceles triangles connected by corners and/or edges.

This was conceived as a false solution for BP898.

Adjacent-numbered pages:
BP892 BP893 BP894 BP895 BP896  *  BP898 BP899 BP900 BP901 BP902

precise, allsorted, notso, traditional, preciseworld

[smaller | same | bigger]

Molly C Klenzak, Aaron David Fairbanks