Solution Insights: Problem on Geometry for 28–01–2022
Published in
Jan 28, 2022
Let us solve a general case of the above problem, where we assume that the Hotel Iota has ‘n’ floors. In such problems, visualization always helps.
Now, it is important to observe that the row ’n’, or the ground floor, has (2n - 1) small triangles as this will help us find P later on. (Fact-1)
Let upward-facing triangles such as in the figure below be called up-triangles.
It is important to note here that each up-triangle is formed by 3 metallic “lines”.
From the figure above, it should be clear that the total number of up-triangles will be
Since each up-triangle is formed by 3 metallic “lines”, clearly
Now, in this particular problem, using (Fact-1) we know that
Accordingly, solve for P and find the answer which is 27.
