1. **State the problem:** Arrange the given statements S1 to S11 in a logical order to form a proof that the probability of a stick broken into three pieces forming a triangle is 1/4. 2. **Identify relevant statements:** The problem involves a stick of length $l$ broken into three parts and uses triangle inequality and geometric probability. 3. **Logical proof arrangement:** - S6: Make an equilateral triangle ABC of side $l$ units, where BC is the stick. - S7: Break the stick into three parts: BX, XY, and YC. - S5: The stick can only break exactly at the midpoints of the triangle. - S4: Let D, E, and F be the midpoints of the sides AB, BC, and CA. - S3: Join D, E, and F to get four smaller equilateral triangles. - S10: The area of the triangle DEF is 1/4 the area of the bigger triangle. - S8: Z will always lie in the triangle DEF. - S9: With XY as the base, make a triangle with the pieces XYZ. - S2: We know from the triangle inequality that the sum of any two sides of a triangle must be greater than the third side. - S1: The length of any piece therefore must be less than $l/2$ units. - S11: The stick is initially made of elastic material, which changes the probability of forming a triangle. 4. **Explanation:** - Start by modeling the stick as side BC of an equilateral triangle ABC (S6). - Break the stick into three parts (S7) at midpoints (S5), which are D, E, F (S4). - Connecting these midpoints forms four smaller equilateral triangles (S3), with DEF having area 1/4 of ABC (S10). - The point Z lies inside DEF (S8), and using XY as base, triangle XYZ is formed (S9). - Triangle inequality (S2) implies each piece length is less than $l/2$ (S1). - Elasticity of the stick affects the probability (S11). 5. **Final answer:** The logical order of statements is S6, S7, S5, S4, S3, S10, S8, S9, S2, S1, S11.