Henry Ernest Dudeney/Puzzles and Curious Problems/240 - Counting the Triangles

Puzzles and Curious Problems by Henry Ernest Dudeney: $240$

Counting the Triangles

Draw a pentagon, and connect each point with every other point with straight lines, as in the diagram.

How many different triangles are contained in this figure?

To make it quite clear, $AFB$, $AGB$, $ACB$, $BFG$, $BFC$, and $BGC$ are six such triangles.

It is not a difficult count if you proceed with some method,

but otherwise you are likely to drop triangles or include some more than once.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $240$. -- Counting the Triangles
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $277$. Counting the Triangles