Henry Ernest Dudeney/Puzzles and Curious Problems/157 - Counting the Matches

Puzzles and Curious Problems by Henry Ernest Dudeney: $157$

Counting the Matches

A friend bought a box of midget matches, each one inch in length.

He found he could arrange them all in the form of a triangle whose area was just as many square inches as there were matches.

He then used up $6$ of the matches,

and found that with the remainder he could again construct a triangle whose area was just as many square inches as there were matches.

And using another $6$ matches he could again do precisely the same.

How many matches were there in the box originally?

The number is less than $40$.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $157$. -- Counting the Matches
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Match Puzzles: $510$. Counting the Matches