On the campus of

# The Three-to-Five Triangle Puzzle

This week’s Puzzle Corner activity comes out of a rich historical tradition that dates back to the 19th century when matches were first manufactured. Invented in 1827 by the British chemist John Walker, matches soon replaced the tinderboxes that people had formerly used to light fires. As matches grew in popularity and became ubiquitous later in the 19th century, they spawned a new form of entertainment—matchstick puzzles—that became quite popular when several match companies printed these puzzles on their boxes. Capitalizing on this interest, publishers began to print books of match-stick puzzles. By the turn of the 20th century, many people had developed a personal repertoire of these puzzles and used them to challenge friends and acquaintances. The toothpick puzzle presented here is modeled after these classical matchstick puzzles, but for safety reasons it uses flat toothpicks instead of matches.

This puzzle may require patience and persistence to solve. It will be a bit easier for any students who have well-developed spatial-relationship skills. Often, these students are not the top students and their ability to solve puzzles like this one faster than their peers is a great esteem builder. Conversely, this type of puzzle often frustrates those students who usually do well at traditional school tasks and provides them with a real challenge. This role reversal has the potential to be beneficial for both sets of students.

Your challenge in this puzzle is to move exactly 3 toothpicks in the following arrangement to make 5 triangles. Good luck!

Solution

Click the arrow below to view the solution.

The challenge was to move only three of those toothpicks to create a total of five triangles. This can be accomplished by moving the triangle on either the left or right above the other two triangles. This gives you four small triangles and a fifth large triangle.

### 4 Responses to The Three-to-Five Triangle Puzzle

1. Deobdre says:

awesome

2. Tracie says:

Claudia,
That was the solution I came up with first as well. 🙂

3. Claudia Rossi says:

If the triangles do not have to be equal there is another solution – use two to bisect two of the triangles and then another to top off the center.

4. Richard Thiessen says:

Great puzzle. I’d never heard the story about the matchstick puzzles printed on match boxes. I have a wooden box with several hundred match sticks for each of which I used a chisel to cut off the business end. I’ve used them with classes for many years, but had no idea about the story of the match boxes. The match sticks are probably a little easier to move around because of the larger diameter, but, of course, it’s a lot of work to chop off the ends.