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

by : $157$

 * 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 $40$.