In the interest of researching what is insufficiently researched, especially in the territory of the Republic of Croatia, this thesis paper presents and deals with the issue of an old but still intriguing problem. More precisely, in the thesis Dudeney's Haberdasher's problem is presented and processed as a problem of dividing an equilateral triangle into the smallest number of parts, whereby a square can be formed without turning over the pieces of the puzzle. Despite countless attempts to solve this problem during the 120 years of its existence, the only valid solution known so far is the solution given by its author back in 1903, one year after the problem was presented. In addition to the description of the construction and the justification of the validity of Dudeney's solution, the thesis paper also considers one solution which, supported by a mathematical proof, turned out to be wrong, and in fact it is only a good approximation of the square. A class of solutions for dividing a triangle into parts that can be shaped into a rectangle, including a square in one special case, was also considered. Furthermore, there are reasons and examples given for why these and similar problems are practical and suitable for use at all levels of education. Part of this thesis paper is devoted to research based on Haberdasher's problem. The conducted research examined different aspects of Haberdasher's problem as an instrument. The results and detailed analysis of the collected data are presented by different variants of the task that was adapted to separate groups of participants.